# Product-perfect Numbers

**Number Theory**Level 4

A number, greater than or equal to 2, is called product-perfect if it is equal to the product of all of its proper divisors. For example, \( 6 = 1 \times 2 \times 3 \), hence \(6\) is product perfect. How many product-perfect numbers are there below \(50\)?

**Details and assumptions**

A **proper divisor** of a number \(N\) is a positive integer less than \( N \) that divides \(N\).