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 $69696% =$ (Error compiling LaTeX. Unknown error_msg)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}$.

2018 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 17	Followed by Problem 19
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All AJHSME/AMC 8 Problems and Solutions

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2018 AMC 8 Problems/Problem 18

Contents

Problem 18

Solution

Solution 2

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