Question

Find the number of divisors of $3600$ excluding one and itself

• A. $44$
• B. $45$
• C. $47$
• D. $43$

Answer 1

The correct option is D $43$

If the prime factorisation of a composite number $N=a^m\times b^n\times c^o....$, the number of its factors $=(m+1)(n+1)(o+1)....$
Prime factorisation of $3600=2^4\times 3^2\times 5^2$
So, number of factors of $3600=(4+1)\times (2+1)\times (2+1)=5\times 3\times 3=45$
From these factors, $1$ and $3600$ are factors too, so remaining number of factors $45-2=43$