Question

The number of even divisors of the number $N=12600=2^3{3}^2{5}^{2}7$ is

• A. $72$
• B. $54$
• C. $18$
• D. None of these

Answer 1

The correct option is B $54$

On prime factorization we have $12600=2^3\times 3^2\times 5^2\times 7.$

Number of factors $=(3+1)(2+1)(2+1)\left(2\right)$

$=72$

Removing power of $2$ remaining factors which are odd $=(2+1)(2+1)\left(2\right)$

$=18$

$\therefore$ Even factors $=72-18=54.$

Hence, the answer is $54.$