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CBSE Questions for Class 6 Maths Playing With Numbers Quiz 3 - MCQExams.com
CBSE
Class 6 Maths
Playing With Numbers
Quiz 3
Which of the following is not a composite number ?
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$$4$$
0%
$$6$$
0%
$$7$$
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$$10$$
Explanation
A composite number is a positive integer that has at least one positive divisor other than one and
number itself.
Here 7 is not composite number as it is cannot be divided evenly orwe can say
7 has divisor 1 and 7 itself that means it is a prime number.
Which list shows the first five multiples of $$2$$?
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$$2, 3, 4, 5, 6$$
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$$2, 4, 6, 8, 10$$
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$$2, 20, 200, 2,000, 20,000$$
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$$2, 22, 222, 2,222, 22,222$$
Explanation
The first $$5$$ multiples of $$2$$ are as follows,
$$2×1=2$$
$$2×2=4$$
$$2×3=6$$
$$2×4=8$$
$$2×5=10$$
Option B has the desired list.
So option B is the correct answer.
Which of the following is not a composite number?
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5
0%
6
0%
7
0%
8
Explanation
A composite number is a positive integer that has at least one positive divisor other than one and number itself.
Here 5 & 7 are not composite number as both cannot be divided evenly.
Smallest $$6$$ digit number divisible by $$6$$ is __________.
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$$100000$$
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$$100002$$
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$$100003$$
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$$100004$$
Explanation
We know that the divisibility test of $$6$$ states that a number is divisible by $$6$$ if the number is even and
the sum of the digits is divisible by
$$3.$$
Hence, $$100002$$ is the smallest number divisible by $$6$$ as it is even and the sum of digits $$1+0+0+0+0+2=3.$$
So, option $$B$$
is correct.
The number which have more than two factors is called _____.
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Even
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Prime
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Odd
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None of these
Explanation
The number with more than two factors is called a composite number.
So option C is the correct answer.
The number of prime numbers between $$0$$ and $$20$$ is
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$$7$$
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$$8$$
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$$6$$
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$$9$$
Explanation
We know that, a prime number is a number having exactly two factors, $$1$$ and the number itself.
Hence, the prime numbers between $$0$$ and $$20$$ are $$2, 3, 5, 7, 11, 13, 17$$ and $$19$$
$$\therefore \ $$ The number of prime numbers between $$0$$ and $$20$$ is $$8.$$
Numbers ending with $$0$$ or $$5$$ are divisible by ___________.
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$$10$$
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$$2$$
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$$5$$
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$$6$$
Explanation
Divisibility of 5 : Numbers ending with 0 and 5 are always divisible by 5
Sum of first three prime numbers which end at 3 is:
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20
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16
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39
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40
Explanation
First three prime numbers which end with $$3$$ are $$3,13,23$$.
$$Sum=3+13+23=39$$
Which of the following pairs are co-prime?
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348 & 296
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59 & 97
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3025 & 4920
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None
Explanation
In number theory, two integers a and b are said to be relatively prime, mutually prime, or coprime if the only positive integer that divides both of them is 1.
Hence answer will be B as there is only one positive integer that divides 59 and 97 is 1.
$$1$$ is a ............ of every prime number.
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factor
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multiple
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both factor and multiple
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none of these
Explanation
$$1$$ is a factor of prime number.
Highest common factor of $$10$$ and $$100$$ is
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$$10$$
0%
$$100$$
0%
$$5$$
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All of the above
Explanation
First we will write $$10$$ and $$100$$ as product of its prime factors,
$$10=5\times 2$$
$$100=5\times 2\times 5\times 2$$
So, from above we can observe that $$5$$ and $$2$$ is common factors,
$$HCF (10,100)= 5\times 2$$
$$=10$$
So, option $$A$$ is correct.
$$21$$ is not co-prime with
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$$3$$
0%
$$7$$
0%
$$22$$
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$$24$$
Explanation
If the H.C.F of two numbers are $$1$$ they are said to be co-prime.
$$21 = 3\times 7$$
$$24 = 8\times 3$$
$$22 = 1\times 11$$
$$21$$ and $$24$$ have common factors $$1$$ and $$3$$.
So, options $$A, B$$ and $$D$$ are correct.
Which of the following numbers are divisible by $$2$$ ?
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$$64$$
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$$16$$
0%
$$32$$
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All of the above
Explanation
Divisibility by 2:
If the number contains an even number (0, 2, 4, 6, 8) in the units place,
then the number is completely divisible by $$2$$.
All the options given here are even numbers i.e $$64$$ ends with $$4$$,
$$16$$ with $$6$$ and $$32$$ ends with $$2$$
So, option D is correct.
Which of the following numbers are divisible by $$2$$?
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$$63$$
0%
$$62$$
0%
$$65$$
0%
$$61$$
Explanation
For a number to be divisible by $$2$$, it must contain an even digit in its unit place.
Since, $$62$$ ends with $$2$$.
Therefore, it is divisible by $$2$$.
So, option B is correct.
The factor(s) of $$59$$ is/are
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$$1$$
0%
$$59$$
0%
$$2$$
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None of these
Explanation
$$59 = 1\times 59$$
$$1$$ and $$59$$ are the factors.
So, options A and B are correct.
Identify co-prime numbers.
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$$(2, 3)$$
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$$(3, 5)$$
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$$(5, 7)$$
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All of the above
Explanation
$$(2, 3)$$ has $$1$$ factor in common
$$(3, 5)$$ has $$1$$ factor in common
$$(5, 7)$$ has $$1$$ factor in common
So, option D is correct.
Co-prime numbers
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have two factors in common
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have one factor in common
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have three factor in common
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none of these
Explanation
Co-prime numbers have one factor in common.
So, option B is correct.
If a number $$N$$ is divisible by $$2$$, then which of the following numbers can be at it's units' position.
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$$0$$
0%
$$1$$
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$$2$$
0%
$$4$$
Explanation
If N is a number divisible by $$2$$,
then the digit in the units place of N should be either $$0, 2, 4, 6$$ or $$8.$$
So, options A, C and D are correct.
The composite numbers _________ .
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has atleast one factors other than itself and 1
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has no factor other than 1
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only A
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none
Explanation
Composite numbers has at least one factor other than itself & 1.
$$21$$ is co-prime with
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$$3$$
0%
$$7$$
0%
$$22$$
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all of the above
Explanation
$$21 = 3\times 7\times 1$$
$$22 = 1\times 2\times 11$$
Only $$1$$ is common, so option $$C$$ is correct.
Which of the following numbers are divisible by $$5$$ ?
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0%
$$10$$
0%
$$100$$
0%
$$1000$$
0%
All of the above
Explanation
A number is divisible by $$5$$, if it contains $$0$$ or $$5$$ in the units place.
Since all the numbers have $$0$$ in the units place,
t
herefore all are divisible by $$5$$.
So, option D is correct.
The product of $$2 \times 7 \times 3 \times 5$$ is a .........
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0%
composite number
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prime number
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negative number
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none of the above
Explanation
Composite numbers are numbers which have more then $$2$$ factors. They have at least $$1$$ factor more than $$1$$ and the number itself.
The given expression has more than $$2$$ factors. So, it is a Composite number.
Therefore, $$A$$ is the correct answer.
Fundamental theorem of arithmetic is when any .......... greater than $$1$$ is either a prime number or can be written as a unique product of prime numbers.
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decimal number
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fraction
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irrational number
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integer
Explanation
Let us take an example, $$15$$ is not a prime number.
$$15 = 3 \times 5$$, where $$3$$ and $$5$$ are prime numbers.
We cannot get the number $$15$$ by multiplying any other prime numbers.
$$15 \neq 2 \times 5 \times 7.$$
It is only with one particular set of prime numbers.
Hence, it is said integers greater than $$1$$ are prime numbers or unique product of prime numbers.
Therefore, $$D$$ is the correct answer.
Every ........ number can be expressed as a product of prime numbers.
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composite
0%
prime
0%
natural
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irrational
Explanation
For example, $$6 = 2\times 3$$, where $$2$$ and $$3$$ are prime numbers.
When we multiply two or more prime numbers we get the product as a composite number.
Therefore, $$A$$ is the correct answer.
Which of the following numbers are divisible by $$3$$ ?
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$$12$$
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$$14$$
0%
$$20$$
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None of the above
Explanation
The sum of the digits of $$12$$ is $$1+2 =3$$.
$$3$$ is divisible by $$3$$
Therefore, $$12$$ is divisible by $$3$$.
So, option A is correct.
Which of the following numbers are divisible by $$9$$ ?
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$$81$$
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$$99$$
0%
$$108$$
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All of the above
Explanation
A number is divisible by $$9$$, if the sum of the digits is also divisible by $$9$$.
Sum of digits of $$81$$ is $$8+1=9$$
Sum of digits of $$99$$ is $$9+9=18$$
Sum of digits of $$108$$ is $$1+0+8=9$$
Thus, all given numbers are divisible by $$9$$
So, option D is correct.
Which of the following number is divisible by $$5 ?$$
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0%
$$63$$
0%
$$65$$
0%
$$64$$
0%
None of the ablove
Explanation
A number is divisible by $$5$$ if it contains $$0$$ or $$5$$ in the units place.
Since only $$65$$ has $$5$$ in the units place,
t
herefore it is divisible by $$5$$.
So, option B is correct.
Which of the following numbers are divisible by $$4$$?
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$$23$$
0%
$$1,216$$
0%
$$1,200$$
0%
$$235$$
Explanation
We know the divisibility rule for $$4$$:
Check the last two digits are a multiple of $$4$$ or if the last two digits are $$00$$.
Here, $$1,216$$ and $$1,200$$ are divisible by $$4$$ because the last two digits are a multiple of $$4$$ and $$00$$ respectively.
So, options B and C are correct.
Choose the number divisible by $$2$$.
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0%
$$12907$$
0%
$$23484$$
0%
$$12971$$
0%
$$34987$$
Explanation
We know the divisibility rule for
2
2
:
The number which is divisible by $$2$$ always end with either $$0, 2, 4, 6$$ or $$8$$
$$12,907$$ ends with $$7$$. So, not divisible by $$2$$
$$12,971$$ ends with $$1$$. So, not divisible by $$2$$
$$34,987$$ ends with $$7$$. So, not divisible by $$2$$
But, $$23,484$$ is divisible by $$2$$ because the last digit is $$4$$.
Which of these numbers are divisible by $$2$$?
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0%
$$1299$$
0%
$$2387$$
0%
$$2091$$
0%
$$3052$$
Explanation
We know the divisibility rule for $$2$$:
Always check the last digit end with $$0, 2, 4, 6$$ or $$8$$.
Here, $$3,052$$ is divisible by $$2$$ because the last digit ends with $$2$$.
So, option D is correct.
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