# Finding Factors

**Number Theory**Level 4

A number of the form: \[2^{a} \times 3^{b} \times 5^{c} \] where a,b and c are all integers, has 103 proper factors

What is the minimum this number can be? \[\]

**Details & Assumptions**

A proper factor is any positive factor of the number not including 1 or the number itself