Class 5 Maths - Be My Multiple I Will Be Your Factor

The product of two numbers is $882$ and their LCM is $126$ . What is the HCF of these numbers?

Given that:

Product of two numbers

$=882$

$LCM$ of the same numbers

$=126$

$HCF=?$

Since we know that,

$HCF\times LCM=$ Product of the numbers

$HCF\times 126=882$

$HCF=\dfrac{882}{126}$

$HCF=7$ .

Hence, the HCF is

$7$ .

Find four common multiples of $8$ and $12$ .

To find common multiples, we need to calculate

$LCM$ of both numbers,

Factors of both numbers are as follows:

$8=2\times2\times2$

$12=2\times2\times3$

Hence,

$LCM=2\times2\times2\times3$

$=24$

Multiples of

$24$ will be common multiples of

$8$ and

$12$ .

Hence, four common multiples of

$8$ and

$12$ are

$24, \ 48,\ 72$ and

$96.$

What is $L.C.M$

$LCM$ stands for least common multiple. The $LCM$ of two numbers is the smallest number that they both divide evenly into.

For example-

$LCM$ of

$2$ and

$3$ is

$6$ .

Write the first ten multiples of $6$ and $8$ .Circle their common multiples.

Multiples of

$6\rightarrow 6, 12, 18, 24, 30, 36, 42, \underline{48}, 54, 60$

Multiples of

$8\rightarrow 3, 16, \underline{24}, 32, 40, \underline{48}, 56, 64, 72, 80$

Common multiples of

$6$ and

$8, 24, 48$

Write the prime factors of $120$

Factors of

$120=2\times 2\times 2\times 3\times 5$

Prime factors

$=\left\{2,\,3,\,5\right\}$

Give two examples of a number which is divisible by:
(a) $3$ but not $9$ (b) $2$ but not $6$ .

a) Two numbers which are divisible by

$3$ but not by

$9$ are

$3,6$ .

b) Two numbers which are divisible by

$2$ but not by

$6$ are

$2,4$ .

Find the following:
$(i)$ the first $15$ multiples of $8$ .
$(ii)$ the first $40$ positive integers divisible by $(a)\,3\,(b)\,5\,(c)\,6$

$(i)$ Multiples of

$8, \quad 8,16,24....8n$

Where

$n\epsilon I,n\epsilon [1,15]$

$(ii) (a)$ Multiples of

$3\quad 3,6,9....3n$

Where

$n\epsilon I,n\epsilon[1,40]$

$(b)$ Multiples of

$5,\quad 5,10,15...5n$

Where

$n\epsilon I,n\epsilon[1,40]$

$(c)$ Multiples of

$6,\quad 6,12,18,24....6n$

Where

$n\epsilon I,n\epsilon [1,40]$

Write down all the factors of the following number
$75$

$75 = 1 \times 75$

$75 = 3 \times 25$

$75 = 5 \times 15$

Hence the factors are

$1, 3, 5, 15, 25$ and

$75$

Write the first six multiples of :
$4$

Following are the first six multiples of

$4$

$1 \times 4 = 4$

$2 \times 4 = 8$

$3 \times 4 = 12$

$4 \times 4 = 16$

$5 \times 4 = 20$

$6 \times 4 = 24$
Hence multiples of

$4$ are

$4 , 8 , 12 , 16 , 20$ and

$24$

Fill in the blanks :
Every number is a multiple of .............

Every number is a multiple of itself

Fill in the blanks :
$x$ is a factor of $y$ , then $y$ is a ........... of $x$ .

$x$ is a factor of

$y$ , then

$y$ is a multiple of

$x$

Write the first six multiples of :
$11$

Following are the six multiples of

$11$

$1 \times 11 = 11$

$2 \times 11 = 22$

$3 \times 11 = 33$

$4 \times 11 = 44$

$5 \times 11 = 55$

$6 \times 11 = 66$
Hence, multiples of

$11$ are

$11 , 22 , 33 , 44 , 55$ and

$66$

Here are factor trees of the number $90$ . Write the missing numbers:

Factor tree of

$90$ :

$5 \times 3 \times 3 \times 2$

1752223_1789090_ans_59778c6954ec46fdae564635e5ca8d6a.png

Write the first six multiples of :
$9$

Following are the first six multiples of

$9$

$1 \times 9 = 9$

$2 \times 9 = 18$

$3 \times 9 = 27$

$4 \times 9 = 36$

$5 \times 9 = 45$

$6 \times 9 = 54$
Hence required multiples of

$9$ are

$9 , 18 , 27 , 36 , 45$ and

$54$

Write the first six multiples of :
$16$

Following are the first six multiples of

$16$

$1 \times 16 = 16$

$2 \times 16 = 32$

$3 \times 16 = 48$

$4 \times 16 = 64$

$5 \times 16 = 80$

$6 \times 16 = 96$
Hence , multiples of

$16$ are

$16 , 32 , 48 , 64 , 80$ and

$96$

Write the first six multiples of :
$15$

Following are the first six multiples of

$15$

$1 \times 15 = 15$

$2 \times 15 = 30$

$3 \times 15 = 45$

$4 \times 15 = 60$

$5 \times 15 = 75$

$6\times 15=90$
Hence , multiples of

$15$ are

$15 , 30 , 45 , 60 , 75$ and

$90$

Determine the prime factorisation of the following positive integer:
(i) $20570$ (ii) $58500$ (iii) $45470971$

$20570=2^1\times5^2\times 11^2\times17 \quad\quad\quad$

$58500={ 2 }^{ 2 }\times { 3 }^{ 2 }\times { 5 }^{ 3 }\times { 13 }^{ 1 }\quad \quad \quad 45470971={ 7 }^{ 2 }\times { 13 }^{ 2 }\times { 17 }^{ 2 }\times { 19 }^{ 1 }$

1225648_964538_ans_3f913389777b497da529257a432072ef.png

Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) $12, 15$ and $21$ (ii) $17, 23$ and $29$ (iii) $8, 9$ and $25$

Using prime factorisation method:

(i) 12, 15 and 21

Factor of

$12 = 2 \times 2 \times 3$

Factor of

$15 = 3 \times 5$

Factor of

$21 = 3 \times 7$

HCF

$(12, 15, 21) = 3$

LCM

$(12, 15, 21) = 2 \times 2 \times 3 \times 5 \times 7 = 420$

(ii) 17, 23 and 29

Factor of

$17 = 1 \times 17$

Factor of

$23 = 1 \times 23$

Factor of

$29 = 1 \times 29$

HCF

$(17, 23, 29) = 1$

LCM

$(17, 23, 29) = 1 \times 17 \times 23 \times 29 = 11,339$

(iii) 8, 9 and 25

Factor of

$8 = 2 \times 2 \times 2 \times 1$

Factor of

$9 = 3 \times 3 \times 1$

Factor of

$25 = 5 \times 5 \times 1$

HCF

$(8, 9, 25) = 1$

LCM

$(8, 9, 25) = 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 = 1,800$

Test each of the following numbers for divisibility by i)3 ii)5 and iii)9.
a. 5049 b. 7705 c. 4265
d. 6990 d. 45350 e. 2391
g. 1475 h. 46299 i. 775

1698444_1026612_ans_4e868ddef1a2415eb21438385e195e4a.jpg

Write the smallest $5$ digit number. Express it in terms of its prime factor by a tree diagram.

We know that,

The smallest five-digit number is $10000.$

Prime factor of $10000=2\times 2\times 2\times 2\times 5\times 5\times 5\times 5$

1016799_1085165_ans_172321a1697b4998a7cf6c9f2b01cf5b.png

Write all the numbers less than $100$ which are common multiples of $3$ and $4$ .

The multiples of 3 less than

$100$ are

$3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99$

multiples of 4 less than

$100$ are

$4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100$

Therefore, the common multiples less than

$100$ are

$12, 24, 36, 48, 60, 72, 84, 96$

Find first three common multiples of :
a) $6$ and $8$
b) $12$ and $18$

A) The multiples of

$6$ are

$0,6,12,18,24,30,36,42,48,...$

The multiples of

$8$ are

$0,8,16,24,32,40,48,56,64,...$

Therefore, the first three common multiples are

$0,24,48$

B) The multiples of

$12$ are

$0,12,24,36,48,60,72,84,96,108,120,132,144,156,168,...$

The multiples of

$18$ are

$0,18,36,54,72,90,108,126,144,162,180,198,216,234,252,,...$

Therefore, the first three common multiples are

$0,36,72$

Write the first five multiples of $10$ and $20$ . Highlight their common multiple and find their LCM.

Multiples of

$10$ :

$10, \textbf{20}, 30, \textbf{40}, 50$

Multiples of

$20$

$\textbf{20}, \textbf{40}, 60, 80, 100$

Common multiples of

$10$ and

$20$ are

$20, 40$

To find

$\text{LCM}$ of

$20$ and

$40$ , we need to write these numbers in the form of product of their prime factors:

$20=2\times 2\times 5=2^2\times 5$

$40=2\times 2\times 2\times 5=2^3\times 5$

$\text{LCM(20,40)}=2\times 2\times 2\times 5$

$=40$ Ans

Define multiple. Give four examples.

Multiple-It is a number which when multiplied with another number produces a given number.

For example-

1. 30 is a multiple of 6 as 6×5=30

2. 45 is a multiple of 5 as 5×9=45

3. 21 is a multiple of 7 as 7×3=21

4. 39 is a multiple of 13 as 13×3=39

Write first five multiplies of the following number.
$25$ .

1504343_1658805_ans_45dabb4fbda44117ac39a901026e62ba.jpg

Write the prime factorisations of $16, 28, 38$ .

$16=2\times2\times2\times2$

$28=2\times2\times2$

$38=2\times19$

Prime factor

$16=2^4$

Prime factor

$28=2^2\times 7$

Prime factor

$38=2\times19$

Write first five multiplies of the following number.
$35$ .

To find first 5 multiples of 35,

35×1=35

35×2=70

35×3=105

35×4=140

35×5=175

So, the first 5 multiples of 35 are 35,70,105,140 and 175

Find first three common multiples of $12$ and $18$ .

${\textbf{Step 1: Find multiples of 12 and 18.}}$

${\text{Multiples of 12 are}} = 12,24,36,48,60,72,84,96,108,120,132,144,.....$

${\text{Multiples of 18 are}} = 18,36,54,{\text{72,90,108,126,144,162,....}}$

${\textbf{Step 3: Find common multiples}}$

${\text{First three common multiples are: }}36,72,108$

${\textbf{First three common multiples of 12 and 18 are: }}\mathbf{36,72,108.}$

Write first five multiplies of the following number.
$40$ .

1503460_1658808_ans_209f166d20cc44f0bdb09c6f714a1f1b.PNG

Write all prime numbers between $40$ and $85$ .

1502692_1658834_ans_5f385613a94c46d59caafdee308d45d2.PNG

Here is different factor tree for $60$ . Writ the missing number.

$3, 2$ are in the blanks.
1517808_1658965_ans_6df30ef0aa564f01b648bda630220406.png

Find first two common multiplies of $12$ and $18$ .

1504675_1658828_ans_39e666cbd9bd4edc84a5b5d445c8d78a.jpg

Factorize the following algebraic expression.
$5(x-2y)^2+3(x-2y)$ .

1686900_1673500_ans_ec75faf98cb44606952f0839375bf1cb.jpg

Factorize the following algebraic expression.
$3a(x-2y)-b(x-2y)$ .

1686910_1673505_ans_bf5b502bcace4902871673d979e278af.jpg

Prove that $\dfrac {1}{9!}+\dfrac {1}{10!}+\dfrac {1}{11!}=\dfrac {122}{11!}$

1407568_1666360_ans_f7f31b097ed2483fb4f86c57366900e4.jpg

Here is different factor trees for $60$ . Write the missing number.

1504907_1658968_ans_d19ce404548940a7bf937cf57a2517a8.png

Fill in the blank.
If the product of two numbers is $360$ and their HCF is $6$ , then their LCM is _______.

The problem can be solved using the property that product of two numbers is equal to the product of HCF and LCM.

Using the above mentioned property:

$HCF\times LCM =360$

$LCM\times 6=360$

$LCM=\dfrac{360}{6}$

$LCM =60$

Hence, the LCM is

$60$ .

Factorize the following algebraic expression.
$9a(6a-5b)-12a^2(6a-5b)$ .

1686897_1673498_ans_1a98b212e1114c9497682c71611d5fb0.jpg

Factorize the following algebraic expression.
$6(a+2b)-4(a+2b)^2$ .

1686946_1673510_ans_c913cd78bdf74a1085ddd089b122645f.jpg

Factorize the following algebraic expression.
$2r(y-x)+s(x-y)$ .

1686887_1673494_ans_7d4fb8dc18ed48d2a6618063831721d0.jpg

Factorize the following algebraic expression.
$a(x-y)+2b(y-x)+c(x-y)^2$ .

1686951_1673514_ans_0f0b23f158be4988b5e45993a9757474.jpg

Factorize the following algebraic expression.
$4(x+y)(3a-b)+6(x+y)(2b-3a)$ .

1686972_1673520_ans_0b92b7f31b70462d9807e244d5c67047.jpg

Factorize the following expression.
$p^2q-pr^2-pq+r^2$ .

1686985_1673525_ans_e302c85c2f6448b5833b2488ed20031b.jpg

Factorize the following expression.
$36l^2-(m+n)^2$ .

1693984_1673606_ans_b5b1a5ee1e6f4db78df66e5c8311f4d9.jpg

Factorize the following expression.
$3a^5-48a^3$ .

1693976_1673602_ans_03abd1affd3a459fa268a4099e9a9e64.jpg

Factorize the following expression.
$(x+2y)^2-4(2x-y)^2$ .

1693975_1673601_ans_0580b5f5477f4be591e3ec2faad2f755.jpg

Factorize the following algebraic expression.
$(2x-3y)(a+b)+(3x-2y)(a+b)$ .

1686957_1673518_ans_2d32dc7db6684575adbce13a1fd6e05a.jpg

Factorize the following expression.
$144a^2-169b^2$ .

1693970_1673598_ans_a81af20b8a034b38badc20f0c647e769.jpg

Factorize the following expression.
$125x^2-45y^2$ .

1693968_1673596_ans_745eb02319ef4b128dab5275aac5842f.jpg

Factorize the following expression.
$x^3-144x$ .

1693989_1673621_ans_4dd2b6e04e4a484ab9cf5929ad81e17c.jpg

Factorize the following expression.
$12m^2-27$ .

1693967_1673594_ans_7a6d1e819ba04f64895d2f381a0ff932.jpg

Factorize the following algebraic expression.
$p^2q^2-6pqr+9r^2$ .

1694048_1673692_ans_09f4b83dfde34e22899497efb57d661d.jpg

Factorize the following algebraic expression.
$36a^2+36a+9$ .

1588622_1673693_ans_9297142b7e454252999754fc0d15e116.jpg

Factorize the following expression.
$(x+y)^2-(a-b)^2$ .

1693995_1673627_ans_f7786737585b4995a7c49d8ae4b3a613.jpg

Factorize the following expression.
$\dfrac{1}{16}x^2y^2-\dfrac{4}{49}y^2z^2$ .

1693997_1673628_ans_86dfcce14611438c8f522961464a072d.jpg

Factorize the following algebraic expression.
$9a^2-24ab+16b^2$ .

1694046_1673689_ans_4426c72027b94e0bbe17c07aec4f429d.jpg

Factorize the following algebraic expression.
$16-a^6+4a^3b^3-4b^6$ .

1588630_1673699_ans_834288a83e3742b2a2388d9954a68fe3.jpg

Factorize the following algebraic expression.
$a^2-2ab+b^2-c^2$ .

1588632_1673702_ans_5b76e534c7cc4f75b219d41e7e865437.jpg

Factorize the following algebraic expression.
$x^2+2x+1-9y^2$ .

1588637_1673703_ans_36dcc2dcd7ba4ff487c1e648a6373a1d.jpg

Factorize the following algebraic expression.
$a^2+2ab+b^2-16$ .

1588624_1673694_ans_49efc84a0b7b48d3ad590bc6c0083245.jpg

Factorize the following algebraic expression.
$9z^2-x^2+4xy-4y^2$ .

1588626_1673696_ans_1366c38b06584d25bf61fa7d3fe2d733.jpg

Factorize the following algebraic expression.
$x^2+9y^2-6xy-25a^2$ .

1588645_1673719_ans_dd1f4583308149c29ef28161a3b9da67.jpg

Factorize the following algebraic expression.
$a^2+4ab+3b^2$ .

1588638_1673705_ans_3dec7d049b9d4c9ab484342b4018a259.jpg

Factorize the following algebraic expression.
$96-4x-x^2$ .

1539513_1673706_ans_4bb2b1e13e9640c48c0b634251868c3d.jpg

Factorize the following algebraic expression.
$4x^4+1$ .

1588639_1673710_ans_895243f53da14346860d99dba38258ab.jpg

Factorize the following algebraic expression.
$(x+2)^2-6(x+2)+9$ .

1539520_1673715_ans_aca0c59464c54fbeaae267beca14e5aa.jpg

Factorize the following algebraic expression.
$a^2-8ab+16b^2-25c^2$ .

1588651_1673724_ans_f246448164b04e009618c9a90692b728.jpg

Factorize the following algebraic expression.
$25-p^2-q^2-2pq$ .

1588644_1673717_ans_760ee8115c364c428b3e615aeb4ecaa4.jpg

Express 360 as product of its prime factors.

$360=3\times 120$

$=3\times 3\times 40$

$=3\times 3\times 2\times 20$

$=3\times 3\times 2\times 2\times 10$

$=3\times 3\times 2\times 2\times 2\times 5$

Find the least multipliers of the number 3675, 4374, 18375, 74088 respectively, which will make the product perfect squares.

1573962_1745430_ans_2c7641130be749ba9a3106df53619bab.png

Find the least multipliers of the numbers 7623, 109350, 539539 respectively, which will make the product perfect cubes.

1573966_1745431_ans_dfc8d5a37a4e46d28c82af00b8b7718e.png

Here are factor trees of the number $90$ . Write the missing numbers:

Factor tree :

$90 = 2 \times 5 \times 3 \times 3$
1752225_1789084_ans_12fad3da56c74963ad73ea5c3ac253d8.png

Write the first five multiples of the following number
$23$

$23 \times 1 = 23$

$23 \times 2 = 46$

$23 \times 3 = 69$

$23 \times 4 = 92$

$23 \times 5 = 115$

$\therefore$ The five multiples of

$23$ are

$23, 46, 69, 92$ and

$115$

If $P$ is prime number then, what is the LCM of $P, \ P^2, \ P^3$ ?

1805425_1784879_ans_169a142ac27e481881a662b8ca3fee77.png

Write the first five multiples of the following number
$70$

$70 \times 1 = 70$

$70 \times 2 = 140$

$70 \times 3 = 210$

$70 \times 4 = 280$

$70 \times 5 = 350$

$\therefore$ The first five factors are

$70, 140, 210, 280$ and

$350$

Write the first five multiples of the following number:
$17$

$17 \times 1 = 17$

$17 \times 2 = 34$

$17 \times 3 = 51$

$17 \times 4 = 68$

$17 \times 5 = 85$

$\therefore$ The first five multiples of

$17$ are

$17, 34, 51, 68$ and

$85$

express each of the following numbers as a product of its prime factors: $5005$

1789069_1814319_ans_85cc31d7e0ad4dd9b12ed8e25ca1effa.png

Find the $LCM$ of $80,96,125,160$

Find the factors of

$80,96,125,160$ ,
The Factors of

$80,96,125$ and

$160$

$=2\times 2\times 2\times 2\times 2\times 3\times 5\times 5\times 5$
Hence the

$LCM$ of

$80,96,125$ and

$160$

$=2\times 2\times 2\times 2\times 2\times 3\times 5\times 5\times 5=12000$
1643804_1788968_ans_c44c79b604594477911cabf4d0d63135.png

Write the first five multiples of the following number
$65$

$65 \times 1 = 65$

$65 \times 2 = 130$

$65 \times 3 = 195$

$65 \times 4 = 260$

$65 \times 5 = 325$

$\therefore$ The first five multiples of

$65$ are

$65, 130, 195, 260$ and

$325$

Write first six multiples of the following natural numbers :
$3$

$3$

The first six multiple of

$3$ are

$3 , 6 , 9 , 12 , 15 , 18$

Find the $LCM$ of $160,170$ and $90$ .

$\textbf{LCM of numbers can be found by multiplying all the prime factors of the numbers, but by}$

$\textbf{considering the common factors of the numbers only once}$ .

Prime factorization of the number

$160 = 2 \times 2 \times 2 \times 2 \times 2 \times 5$

$170 = 2 \times 5 \times 17$

$90 = 2 \times 3 \times 3 \times 5$

$\therefore$ LCM

$= 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 17$

$= 24480$

$\textbf{Hence, the LCM of 160, 170, 90 is 24480}$

Find the highest power of $5$ in $23750$ .

To find the highest power of

$5$ in

$23750$ , we have to factorize

$23750$ .

1789079_1814337_ans_440e4d4af5b046ef914bf725847caa6a.PNG

Express each of the following numbers as a product of its prime factors: $32760$ .

1789072_1814324_ans_64e2b5c265064f90b3a2119199b26dfd.PNG

Express each of the following numbers as a product of its prime factors: $156$ .

1789073_1814327_ans_54786240c5ae4a15b2f45b65c97230cc.png

Write down the missing numbers $a,b,c,d,x,y$ in the above factor tree.

1789102_1814389_ans_b6abad3fbb794a00bafbd346fe57cb9e.png

Write down the missing numbers $a,b,c,d,x,y$ in the above factor tree:

1789423_1814403_ans_32a4d59d811943a0ae382c775bd94d22.png

Find the highest power of $2$ in $1440$ .

Given number is

$1440$

Factorization of

$1440$ is

1789081_1814366_ans_2814d27a2bb24671895e0de775cb35a8.PNG

Write down the missing numbers $a,b,c,d,x,y$ in the above factor tree:

1789104_1814393_ans_adc14982fa174c1e800b1267bc721d1e.png

Using the common multiple method, find the L.C.M. of the following:
$10, 15$ and $20$

$10, 15$ and

$20$

2 10 15 20

2 5 15 10

3 5 15 5

5 5 5 5

1 1 1

We get,

$L.C.M = 2 × 2 × 3 × 5$

$= 60$

Hence,

$L.C.M.$ of

$10, 15$ and

$20 = 60$

Write down the missing numbers $a,b,c,d,x,y$ in the above factor tree:

1789379_1814399_ans_73456ec11b6045f0be18d71f3f7c3aea.png

Express each of the following numbers as a product of its prime factors: $729$ .

1789075_1814333_ans_364af81d0c42410082b8ed0827b3cc39.PNG

Using the common multiple method, find the L.C.M. of the following:
$3, 6, 9$ and $12$

$3, 6, 9$ and

$12$

2 3, 6, 9, 12

2 3, 3, 9, 6

3 3, 3, 9, 3

3 1, 1, 3, 1

1, 1, 1, 1

We get,

$L.C.M. = 2 × 2 × 3 × 3$

$= 36$

Hence,

$L.C.M.$ of

$3, 6, 9$ and

$12 = 36$

Here are two different factor trees for $60$ write the missing numbers.

1879109_1866601_ans_fffc95eee4a6434283dc4d0a25200acb.png

Write first $10$ number which are common multiples of $3$ and $4$

Multiples of

$3=3,6,0,12,15,18,21,24,27,30$
Multiples of

$4= 4,8,12,16,20,24,28,32,36,40$
Common multiples=

$12,24,36,48,60,72,84,96$

Find the value of a in the factor tree.

$2 \times 5 = 10$

$10 \times 2 = 20$

$20 \times 5 = 100$
∴

$a= 100$

Factorize the following algebraic expression.
$-4(x-2y)^2+8(x-2y)$ .

2184946_1673515_ans_89905c8462be4611bee7837ddd845908.jpeg

Factorize the following algebraic expression.
$4x^4+y^4$ .

1539518_1673713_ans_96a4ac5b8fd24d9eb61367c29bd048f8.jpg

Be My Multiple I Will Be Your Factor - Class 5 Maths - Extra Questions

The product of two numbers is 882882 and their LCM is 126126. What is the HCF of these numbers?

Find four common multiples of 88 and 1212.

What is L.C.ML.C.M

Write the first ten multiples of 66 and 88.Circle their common multiples.

Write the prime factors of 120120

Give two examples of a number which is divisible by:(a) 33 but not 99 (b) 22 but not 66.

Find the following:(i)(i) the first 1515 multiples of 88.(ii)(ii) the first 4040 positive integers divisible by (a)3(b)5(c)6(a)\,3\,(b)\,5\,(c)\,6

Write down all the factors of the following number7575

Write the first six multiples of : 44

Fill in the blanks :Every number is a multiple of .............

Fill in the blanks :xx is a factor of yy , then yy is a ........... of xx .

Write the first six multiples of : 1111

Here are factor trees of the number 90 90 . Write the missing numbers:

Write the first six multiples of : 99

Write the first six multiples of : 1616

Write the first six multiples of : 15 15

Determine the prime factorisation of the following positive integer:(i) 2057020570 (ii) 5850058500 (iii) 4547097145470971

Find the LCM and HCF of the following integers by applying the prime factorisation method.(i) 12,1512, 15 and 2121 (ii) 17,2317, 23 and 2929 (iii) 8,98, 9 and 2525

Test each of the following numbers for divisibility by i)3 ii)5 and iii)9.a. 5049 b. 7705 c. 4265d. 6990 d. 45350 e. 2391g. 1475 h. 46299 i. 775

Write the smallest 55 digit number. Express it in terms of its prime factor by a tree diagram.

Write all the numbers less than 100100 which are common multiples of 33 and 44.

Find first three common multiples of :a) 66 and 88b) 1212 and 1818

Write the first five multiples of 1010 and 2020. Highlight their common multiple and find their LCM.

Define multiple. Give four examples.

Write first five multiplies of the following number.2525.

Write the prime factorisations of 16,28,3816, 28, 38.

Write first five multiplies of the following number.3535.

Find first three common multiples of 1212 and 1818.

Write first five multiplies of the following number.4040.

Write all prime numbers between 4040 and 8585.

Here is different factor tree for 6060. Writ the missing number.

Find first two common multiplies of 1212 and 1818.

Factorize the following algebraic expression.5(x−2y)2+3(x−2y)5(x-2y)^2+3(x-2y).

Factorize the following algebraic expression.3a(x−2y)−b(x−2y)3a(x-2y)-b(x-2y).

Prove that 19!+110!+111!=12211!\dfrac {1}{9!}+\dfrac {1}{10!}+\dfrac {1}{11!}=\dfrac {122}{11!}

Here is different factor trees for 6060. Write the missing number.

Fill in the blank.If the product of two numbers is 360360 and their HCF is 66, then their LCM is _______.

Factorize the following algebraic expression.9a(6a−5b)−12a2(6a−5b)9a(6a-5b)-12a^2(6a-5b).

Factorize the following algebraic expression.6(a+2b)−4(a+2b)26(a+2b)-4(a+2b)^2.

Factorize the following algebraic expression.2r(y−x)+s(x−y)2r(y-x)+s(x-y).

Factorize the following algebraic expression.a(x−y)+2b(y−x)+c(x−y)2a(x-y)+2b(y-x)+c(x-y)^2.

Factorize the following algebraic expression.4(x+y)(3a−b)+6(x+y)(2b−3a)4(x+y)(3a-b)+6(x+y)(2b-3a).

Factorize the following expression.p2q−pr2−pq+r2p^2q-pr^2-pq+r^2.

Factorize the following expression.36l2−(m+n)236l^2-(m+n)^2.

Factorize the following expression.3a5−48a33a^5-48a^3.

Factorize the following expression.(x+2y)2−4(2x−y)2(x+2y)^2-4(2x-y)^2.

Factorize the following algebraic expression.(2x−3y)(a+b)+(3x−2y)(a+b)(2x-3y)(a+b)+(3x-2y)(a+b).

Factorize the following expression.144a2−169b2144a^2-169b^2.

Factorize the following expression.125x2−45y2125x^2-45y^2.

Factorize the following expression.x3−144xx^3-144x.

Factorize the following expression.12m2−2712m^2-27.

Factorize the following algebraic expression.p2q2−6pqr+9r2p^2q^2-6pqr+9r^2.

Factorize the following algebraic expression.36a2+36a+936a^2+36a+9.

Factorize the following expression.(x+y)2−(a−b)2(x+y)^2-(a-b)^2.

Factorize the following expression.116x2y2−449y2z2\dfrac{1}{16}x^2y^2-\dfrac{4}{49}y^2z^2.

Factorize the following algebraic expression.9a2−24ab+16b29a^2-24ab+16b^2.

Factorize the following algebraic expression.16−a6+4a3b3−4b616-a^6+4a^3b^3-4b^6.

Factorize the following algebraic expression.a2−2ab+b2−c2a^2-2ab+b^2-c^2.

Factorize the following algebraic expression.x2+2x+1−9y2x^2+2x+1-9y^2.

Factorize the following algebraic expression.a2+2ab+b2−16a^2+2ab+b^2-16.

Factorize the following algebraic expression.9z2−x2+4xy−4y29z^2-x^2+4xy-4y^2.

Factorize the following algebraic expression.x2+9y2−6xy−25a2x^2+9y^2-6xy-25a^2.

Factorize the following algebraic expression.a2+4ab+3b2a^2+4ab+3b^2.

Factorize the following algebraic expression.96−4x−x296-4x-x^2.

Factorize the following algebraic expression.4x4+14x^4+1.

Factorize the following algebraic expression.(x+2)2−6(x+2)+9(x+2)^2-6(x+2)+9.

Factorize the following algebraic expression.a2−8ab+16b2−25c2a^2-8ab+16b^2-25c^2.

Factorize the following algebraic expression.25−p2−q2−2pq25-p^2-q^2-2pq.

Express 360 as product of its prime factors.

Find the least multipliers of the number 3675, 4374, 18375, 74088 respectively, which will make the product perfect squares.

Find the least multipliers of the numbers 7623, 109350, 539539 respectively, which will make the product perfect cubes.

Here are factor trees of the number 90 90 . Write the missing numbers:

Write the first five multiples of the following number2323

If PP is prime number then, what is the LCM of P, P2, P3P, \ P^2, \ P^3?

Write the first five multiples of the following number7070

Write the first five multiples of the following number:1717

express each of the following numbers as a product of its prime factors: 50055005

Find the LCMLCM of 80,96,125,16080,96,125,160

Write the first five multiples of the following number6565

The product of two numbers is $882$ and their LCM is $126$ . What is the HCF of these numbers?

Find four common multiples of $8$ and $12$ .

What is $L.C.M$

Write the first ten multiples of $6$ and $8$ .Circle their common multiples.

Write the prime factors of $120$

Give two examples of a number which is divisible by:
(a) $3$ but not $9$ (b) $2$ but not $6$ .

Find the following:
$(i)$ the first $15$ multiples of $8$ .
$(ii)$ the first $40$ positive integers divisible by $(a)\,3\,(b)\,5\,(c)\,6$

Write down all the factors of the following number
$75$

Write the first six multiples of :
$4$

Fill in the blanks :
Every number is a multiple of .............

Fill in the blanks :
$x$ is a factor of $y$ , then $y$ is a ........... of $x$ .

Write the first six multiples of :
$11$

Here are factor trees of the number $90$ . Write the missing numbers:

Write the first six multiples of :
$9$

Write the first six multiples of :
$16$

Write the first six multiples of :
$15$

Determine the prime factorisation of the following positive integer:
(i) $20570$ (ii) $58500$ (iii) $45470971$

Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) $12, 15$ and $21$ (ii) $17, 23$ and $29$ (iii) $8, 9$ and $25$

Test each of the following numbers for divisibility by i)3 ii)5 and iii)9.
a. 5049 b. 7705 c. 4265
d. 6990 d. 45350 e. 2391
g. 1475 h. 46299 i. 775

Write the smallest $5$ digit number. Express it in terms of its prime factor by a tree diagram.

Write all the numbers less than $100$ which are common multiples of $3$ and $4$ .

Find first three common multiples of :
a) $6$ and $8$
b) $12$ and $18$

Write the first five multiples of $10$ and $20$ . Highlight their common multiple and find their LCM.

Write first five multiplies of the following number.
$25$ .

Write the prime factorisations of $16, 28, 38$ .

Write first five multiplies of the following number.
$35$ .

Find first three common multiples of $12$ and $18$ .

Write first five multiplies of the following number.
$40$ .

Write all prime numbers between $40$ and $85$ .

Here is different factor tree for $60$ . Writ the missing number.

Find first two common multiplies of $12$ and $18$ .

Factorize the following algebraic expression.
$5(x-2y)^2+3(x-2y)$ .

Factorize the following algebraic expression.
$3a(x-2y)-b(x-2y)$ .

Prove that $\dfrac {1}{9!}+\dfrac {1}{10!}+\dfrac {1}{11!}=\dfrac {122}{11!}$

Here is different factor trees for $60$ . Write the missing number.

Fill in the blank.
If the product of two numbers is $360$ and their HCF is $6$ , then their LCM is _______.

Factorize the following algebraic expression.
$9a(6a-5b)-12a^2(6a-5b)$ .

Factorize the following algebraic expression.
$6(a+2b)-4(a+2b)^2$ .

Factorize the following algebraic expression.
$2r(y-x)+s(x-y)$ .

Factorize the following algebraic expression.
$a(x-y)+2b(y-x)+c(x-y)^2$ .

Factorize the following algebraic expression.
$4(x+y)(3a-b)+6(x+y)(2b-3a)$ .

Factorize the following expression.
$p^2q-pr^2-pq+r^2$ .

Factorize the following expression.
$36l^2-(m+n)^2$ .

Factorize the following expression.
$3a^5-48a^3$ .

Factorize the following expression.
$(x+2y)^2-4(2x-y)^2$ .

Factorize the following algebraic expression.
$(2x-3y)(a+b)+(3x-2y)(a+b)$ .

Factorize the following expression.
$144a^2-169b^2$ .

Factorize the following expression.
$125x^2-45y^2$ .

Factorize the following expression.
$x^3-144x$ .

Factorize the following expression.
$12m^2-27$ .

Factorize the following algebraic expression.
$p^2q^2-6pqr+9r^2$ .

Factorize the following algebraic expression.
$36a^2+36a+9$ .

Factorize the following expression.
$(x+y)^2-(a-b)^2$ .

Factorize the following expression.
$\dfrac{1}{16}x^2y^2-\dfrac{4}{49}y^2z^2$ .

Factorize the following algebraic expression.
$9a^2-24ab+16b^2$ .

Factorize the following algebraic expression.
$16-a^6+4a^3b^3-4b^6$ .

Factorize the following algebraic expression.
$a^2-2ab+b^2-c^2$ .

Factorize the following algebraic expression.
$x^2+2x+1-9y^2$ .

Factorize the following algebraic expression.
$a^2+2ab+b^2-16$ .

Factorize the following algebraic expression.
$9z^2-x^2+4xy-4y^2$ .

Factorize the following algebraic expression.
$x^2+9y^2-6xy-25a^2$ .

Factorize the following algebraic expression.
$a^2+4ab+3b^2$ .

Factorize the following algebraic expression.
$96-4x-x^2$ .

Factorize the following algebraic expression.
$4x^4+1$ .

Factorize the following algebraic expression.
$(x+2)^2-6(x+2)+9$ .

Factorize the following algebraic expression.
$a^2-8ab+16b^2-25c^2$ .

Factorize the following algebraic expression.
$25-p^2-q^2-2pq$ .

Here are factor trees of the number $90$ . Write the missing numbers:

Write the first five multiples of the following number
$23$

If $P$ is prime number then, what is the LCM of $P, \ P^2, \ P^3$ ?

Write the first five multiples of the following number
$70$

Write the first five multiples of the following number:
$17$

express each of the following numbers as a product of its prime factors: $5005$

Find the $LCM$ of $80,96,125,160$

Write the first five multiples of the following number
$65$

Write first six multiples of the following natural numbers :
$3$

Find the $LCM$ of $160,170$ and $90$ .

Find the highest power of $5$ in $23750$ .

Express each of the following numbers as a product of its prime factors: $32760$ .

Express each of the following numbers as a product of its prime factors: $156$ .