Question

In how many ways the number $10800$ can be resolved as a product of two factors.

Answer 1

Step 1: Prime factorization of $10800$ i.e. we write $10800=2^4\times 3^2\times 5^3$

Step 2: Number of factors of $10800$ will be $(4+1)(2+1)(3+1)=5\times 3\times 4=60$

Step 3: Hence number of ways to express $10800$ as a product of two numbers is exactly half its number of factors i.e.$\frac{1}{2}\times 60=30$