Question

Consider the number $N=2910600$. Total number of divisors of N, which are divisible by $15$ but not by $36$ are.

• A. $72$
• B. $94$
• C. $96$
• D. $98$

Answer 1

The correct option is A $72$

Given number

$N=2910600=2^3\times 3^3\times 5^2\times 7^2\times 11$

$N$ is divisible by $15$ not by $36=2^2\times 3^2$

Hence The number should not contain $2^2$ or more

So number of ways of power of $2$ is $2^0,2^1$

So number of ways of power of $3$ is $3^1,3^2,3^3$

So number of ways of power of $5$ is $5^1,5^2$

So number of ways of power of $7$ is $7^0,7^1,7^2$

So number of ways of power of $1$ is ${11}^0,{11}^1$

Hence total number of ways are $=2\times 3\times 2\times 3\times 2=72$