Question

How many divisors of 21600 are divisible by 10 but not by 15?

• A. $10$
• B. $30$
• C. $40$
• D. none

Answer 1

Answer: (A)

$10$

On prime factorizing $21600$ we get,

$\Rightarrow 21600=2^5\times 3^3\times 5^2$

Applying condition given in question we can tell that number must be divisible by both $2$ and $5$ and not by $3$.

i.e. divisor are of for $2^a{5}^b$

$a\in (1,.......5)b(1,2)$

So total combination $5\times 2$

$=10.$

Hence the answer is $10.$