# 2018 AMC 8 Problems/Problem 18

## Problem 18

How many positive factors does 23,232 have?

$\textbf{(A) }9\qquad\textbf{(B) }12\qquad\textbf{(C) }28\qquad\textbf{(D) }36\qquad\textbf{(E) }42$

## Solution

We can first find the prime factorization of $23,232$, which is $2^6\cdot3^1\cdot11^2$. Now, we just add one to our powers and multiply. Therefore, the answer is $(6+1)\cdot(1+1)\cdot(2+1)=7\cdot2\cdot3=\boxed{\textbf{(E) }42}$

## Solution 2

Observe that 69696 = 264^2$, so this is$\frac{1}{3}$of$264^2$which is$88 \cdot 264 = 11^2 \cdot 8^2 \cdot 3 = 11^2 \cdot 2^6 \cdot 3$, which has$3 \cdot 7 \cdot 2 = 42$factors. The answer is$\boxed{\textbf{(E) }42}\$.