Question

In how many ways can $2304$ be written as product of two different factors?

• A. $27$
• B. $14$
• C. $13$
• D. $28$

Answer 1

The correct option is C $13$

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 $2304=2^8\times 3^2$
So, number of factors of $2304=(8+1)\times (2+1)=9\times 3=27$
If a number is a perfect square, number of ways it can be written as a product of two factors $=\frac{No.offactors+1}{2}=\frac{27+1}{2}=14$
But from these pairs of factors, one pair is $48\times 48$
So, number of ways $2304$ can be written as a product of two factors is $14-1=13$