2022 AMC 8 Problem 3 - Math Gold Medalist

Lor

2022 AMC 8

Problem 3

When three positive integers $a$ , $b$ , and $c$ are multiplied together, their product is $100$ . Suppose $a < b < c$ . In how many ways can the numbers be chosen?

$\textbf{(A) } 0 \qquad \textbf{(B) } 1\qquad\textbf{(C) } 2\qquad\textbf{(D) } 3\qquad\textbf{(E) } 4$

Related Ideas

Casework

Priority : The Most Limited Case

Hint

Consider cases of c first