Given a number N=4200 , then the number of divisor of N which are neither divisible by 3 nor by 5 is

Question

Given a number N=4200 , then the number of divisor of N which are neither divisible by 3 nor by 5 is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

4200=42× 100=(2 × 3 × 7)(22 × 52) ⇒ 4200=23⋅ 31⋅ 52⋅ 71 If divisor is neither divisible by 3 nor by 5 , then it should not have any power of 3 as well as 5 . Number of divisors =(3 + 1)(1)(1)(1 + 1)=8

Q. Given a number $N = 4200$ , then the number of divisor of $N$ which are neither divisible by $3$ nor by $5$ is

$4200 = 42 \times 100 = (2 \times 3 \times 7) (2^{2} \times 5^{2})$
$\Rightarrow 4200 = 2^{3} \cdot 3^{1} \cdot 5^{2} \cdot 7^{1}$
If divisor is neither divisible by $3$ nor by $5$ , then it should not have any power of $3$ as well as $5$ .
Number of divisors $= (3 + 1) (1) (1) (1 + 1) = 8$

Q. Given a number N=4200 , then the number of divisor of N which are neither divisible by 3 nor by 5 is

4200=42×100=(2×3×7)(22×52) ⇒4200=23⋅31⋅52⋅71 If divisor is neither divisible by 3 nor by 5 , then it should not have any power of 3 as well as 5 . Number of divisors =(3+1)(1)(1)(1+1)=8

Q. Given a number $N = 4200$ , then the number of divisor of $N$ which are neither divisible by $3$ nor by $5$ is

$4200 = 42 \times 100 = (2 \times 3 \times 7) (2^{2} \times 5^{2})$
$\Rightarrow 4200 = 2^{3} \cdot 3^{1} \cdot 5^{2} \cdot 7^{1}$
If divisor is neither divisible by $3$ nor by $5$ , then it should not have any power of $3$ as well as $5$ .
Number of divisors $= (3 + 1) (1) (1) (1 + 1) = 8$