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CBSE Questions for Class 6 Maths Playing With Numbers Quiz 10 - MCQExams.com

Find the all the factors of

$39$

0%
$1, 3, 13, 39$
0%
$1, 3, 39$
0%
$1, 3, 13$
0%
$3, 13, 39$

Using the divisibility test, determine which of the following numbers are divisible by

$2.$

0%
$2144$
0%
$1258$
0%
$4336$
0%
$633$
0%
$1352$

Explanation

For the number to be divisible by

$2$ , the last digit should be even.

$A) 2144$

The last digit of the given number is

$4$ , which is even. Therefore, the number is divisible by

$2.$

$B) 1258$

The last digit of the given number is

$8$ , which is even. Therefore, the number is divisible by

$2.$

$C) 4336$

The last digit of the given number is

$6,$ which is even. Therefore, the number is divisible by

$2.$

$D) 633$

The last digit of the given number is

$3,$ which is odd. Therefore, the number is not divisible by

$2.$

$E) 1352$

The last digit of the given number is

$2,$ which is even. Therefore, the number is divisible by

$2.$

Which one of the following is a common factor of

$15$ and

$12$ .

0%
$2$
0%
$4$
0%
$5$
0%
$3$

The least number of 4-digits which is exactly divisible by 9 is

0%
1008
0%
1009
0%
1026
0%
1018

Explanation

We use a rule to check whether the number is divisible by 9 or not.

A number is divisible by 9 if the sum of the digits is evenly divisible by 9.

Sum of digits of

$1008$ is

$1+0+0+8=9$ , which is divisible by 9 hence

$1008$ is divisible by 9.

State true(T) or false(F).
The sum of primes cannot be a prime.

0%
True
0%
False

Explanation

This statement is also false.

As consider, the numbers

$2$ and

$3$ then sum of

$2$ and

$3$ i.e. is

$5$ is also a prime number.

State true or false:
The product of primes cannot be a prime.

0%
True
0%
False

Explanation

The product of two primes can't be a prime because it violates the definition of the prime number as it will be divided by the prime numbers which are multiplied rather than

$1$ and the number itself. So the number is not prime it will become a composite number instead.

State true(T) or false(F).
Odd numbers cannot be composite.

0%
True
0%
False

Explanation

The given statement is false.

As, consider the number

$9$ , which is an odd number and it is a composite number too.

Since

$3$ divides the given number.

So

$3$ is a divisor of

$9$ other than

$1$ and

$9$ .

Which of the following pairs are always co-primes?

0%
Two prime numbers
0%
One prime and one composite number
0%
Two composite numbers
0%
None of the above

State true(T) or false(F).
An even number is composite.

0%
True
0%
False

Explanation

This statement is also false.

Since

$2$ is the number which is both even and prime.

Hence an even number may not be composite.

State true of false:
If two numbers are co-prime, at least one of them must be a prime number.

0%
True
0%
False

Explanation

The given statement is not correct as consider the numbers

$8$ and

$9$ they are co-prime as HCF of them is

$1$ but neither of them are prime.

Choose a perfect number:

0%
$16$
0%
$8$
0%
$24$
0%
$28$

Explanation

The proper divisors of

$28$ are

$, 2, 4, 7, 14$

Now their sum

$1+2+4+7+14 = 28$

Hence,

$28$ is a perfect number.

The least prime is?

0%
$1$
0%
$2$
0%
$3$
0%
$5$

Explanation

The number

$2$ is the least prime. It is the only even prime also.

Which one of the following numbers is divisible by

$3$ ?

0%
$27326$
0%
$42356$
0%
$73545$
0%
$45326$

Explanation

We use a rule to check whether the number is divisible by 3 or not.

A number is divisible by 3 if the sum of the digits is evenly divisible by 3.

Sum of digits divisible by

$3$

A)

$2 + 7 + 3 + 2 + 6 = 20$

B)

$4 + 2 + 3 + 5 + 6 = 20$

C)

$7 + 3 + 5 + 4 + 5 = 24$

D)

$4 + 5 + 3 + 2 + 6 = 20$

Only C)

$24$ is divisible by

$3$

So, option C is the correct option.

Which of the following are co-primes?

0%
$8, 10$
0%
$9, 10$
0%
$6, 8$
0%
$15, 18$

Explanation

If the H.C.F of two numbers are

$1$ they are said to be co-prime

Factors of

$9=1,3$

Factors of

$10=1,2,5$

$\Rightarrow$ Common factor

$=1$

$\therefore$

$(9, 10)$ is pair of co-prime.

Which of the following number is divisible by

$4$ ?

0%
$8675231$
0%
$9843212$
0%
$1234567$
0%
$543123$

Explanation

Rule to check whether the number is divisible by 4 or not is as follows:

Suppose we have a number is

$abcde$ ,

then if

$de$ is divisible by

$4$ , then the whole number is divisible by

$4$ .

We work on each option and use above rule to find which of the given options is divisible by 4.

A.

$8675231$

31 is not divisible by 4. So,

$8675231$ is also not divisible by

$4$ .

B.

$9843212$

12 is divisible by 4. So,

$9843212$ is also divisible by

$4$ .

$\textbf{So, Option B is correct}$

C.

$1234567$

67 is not divisible by 4. So,

$1234567$ is also not divisible by

$4$ .

D.

$543123$

23 is not divisible by 4. So,

$543123$ is also not divisible by

$4$ .

The total number of even prime numbers is?

0%
$0$
0%
$1$
0%
$2$
0%
Unlimited

Explanation

The number

$2$ is the only prime number, which is even. So, the number of even primes is equal to

$1$ .

Choose the perfect number:

0%
$4$
0%
$12$
0%
$8$
0%
None of these

Mark the correct alternative of the following.
Which of the following is a prime number?

0%
$263$
0%
$361$
0%
$323$
0%
$324$

Which of the following number/s is/are divisible by

$6$ ?

0%
$7908432$
0%
$68719402$
0%
$45982014$
0%
None of the above

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

$3$ .

As all the options are even they all are divisible by

$2.$

Now we will check the sum of digits of numbers:

A)

$7 + 9 + 0 + 8 + 4 + 3 + 2 = 33$

B)

$6 + 8 + 7 + 1 + 9 + 4 + 0 + 2 = 37$

C)

$4 + 5 + 9 + 8 + 2 + 0 + 1 + 4 = 33$

As

$33$ is divisible by

$3$ so A) and C) are divisible by

$3$

So options A and C are divisible by

$6$

option A, C are correct options

Mark the correct alternative of the following.
Which of the following numbers is prime?

0%
$23$
0%
$51$
0%
$38$
0%
$26$

Which of the following numbers is divisible by

$8$ ?

0%
$87653234$
0%
$78956042$
0%
$64298602$
0%
$98741032$

Explanation

To check if a number is divisible by

$8$ , we check if the last three digits of the number is divisible by

$8$ .

Last

$3$ digits of the given numbers are:

A.

$234$

B.

$042$

C.

$602$

D.

$032$

We see that the only number divisible by

$8$ is

$032$ .

$\therefore \ 98741032$ is the only number divisible by

$8$ .

Hence, option D is correct.

Mark the correct alternative of the following.
From the numbers

$2, 3, 4, 5, 6, 7, 8, 9$ how many pairs of co-primes can be formed?

0%
$19$
0%
$18$
0%
$20$
0%
$21$

Explanation

If the H.C.F of two numbers are

$1$ they are said to be co-prime

The following are the pairs of co-prime numbers:

$(2,3), (2,5), (2,7), (2,9), (3,4), (3,5), (3,7), (3,8), (4,5), (4,7), (4,9), (5,6), (5,7), (5,8), (5,9), (6,7), (7,8), (7,9), (8,9).$

Number of pairs of co-prime numbers are

$19.$

Mark the correct alternative of the following.
The smallest number which is neither prime nor composite is?

0%
$0$
0%
$1$
0%
$2$
0%
$3$

If a and b are two co-primes, then which of the following is/are true?

0%
LCM(a, b) $=a\times b$
0%
HCF(a, b) $=1$
0%
Both (a) and (b)
0%
Neither (a) nor (b)

Explanation

Given

$a,b$ are two co-primes then HCF

$(a,b)=1$ [ Definition of co-primes].

We've,

LCM

$\times$ HCF

$=a\times b$

or, LCM

$=a\times b$ . [ Since HCF

$=1$ ]

HCF of

$144$ and

$198$ is

0%
$9$
0%
$18$
0%
$6$
0%
$12$

Explanation

$\textbf{Step 1: Calculate Common Factors of 144 and 198}$

$\text{Prime Factors of 144 and 198 are:}$

$198 = 2 \times 3\times3 \times 11$

$144 = 2\times2\times2\times2 \times 3\times3$

$\Rightarrow \text{Common factor of 198 and 144 =}$

$(3\times 3)$

$\therefore\text{HCF=9}$

$\textbf{Thus, HCF of 198 and 144 is 9}$

Which of the following numbers is divisible by

$3$ ?

0%
$24357806$
0%
$35769812$
0%
$83479560$
0%
$3336433$

Explanation

We use a rule to check whether the number is divisible by 3 or not.

A number is divisible by 3 if the sum of the digits is evenly divisible by 3.

Since sum of its digits

$= 8 + 3 + 4 + 7 + 9 + 5 + 6 + 0 = 42$

$42$ is divisible by

$3$
Option (c) is the correct answer

Which of the following numbers is divisible by

$4$ ?

0%
$78653234$
0%
$98765042$
0%
$24689602$
0%
$87941032$

Explanation

A number is divisible by

$4$ if the number formed

by the digits in

$\text{units and tens}$ places

is divisible by

$4$ .

Since the number formed by tens and ones digits is divisible by

$4$ i.e.

$32$

$32 \div 4 = 8$
Option (d) is the correct answer

Which of the following number is divisible by

$8$ ?

0%
$96354142$
0%
$37450176$
0%
$57064214$
0%
none of these

Explanation

To check if a number is divisible by

$8$ , we check if the last three digits of the number is divisible by

$8$ .
Since the number formed by hundreds tens and one’s digits is divisible by

$8$ i.e.

$176$

$176 \div 8 = 22$
Option (b) is the correct answer

State whether the following statements are true (T) or false (F):
A natural number is called a composite number if it has at least one more factor other than

$1$ and the number itself.

0%
True
0%
False

Which of the following are co-primes?

0%
$39,91$
0%
$161,192$
0%
$385,462$
0%
none of these

Explanation

If the H.C.F of two numbers are

$1$ they are said to be co-prime.

$\therefore$

$(14,35)$ is not pair of co-prime.

a)

$39, 91$
Since

$39, 91$ have common factor

$13$
Hence

$39, 91$ are not co-primes
b)

$161, 192$
Since

$161, 192$ have no common factor other than

$1$ itself
Hence

$161, 192$ are co-primes
c)

$385, 462$
Since

$385, 462$ have common factors

$7$ and

$11$
Hence

$385, 462$ are not co-primes
Option (b) is the correct answer

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