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2021 GMC 10B Problems/Problem 3

Revision as of 14:19, 6 March 2022 by Pineconee (talk | contribs) (Created page with "==Problem== What is the sum of the digits of the largest prime that divides <math>32160</math>? <math>\textbf{(A)} ~3 \qquad\textbf{(B)} ~7 \qquad\textbf{(C)} ~9 \qquad\textb...")
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Problem

What is the sum of the digits of the largest prime that divides $32160$?

$\textbf{(A)} ~3 \qquad\textbf{(B)} ~7 \qquad\textbf{(C)} ~9 \qquad\textbf{(D)} ~11\qquad\textbf{(E)} ~13$

Solution

Prime Factorizing $32160$, we have \[32160 = 2^5\cdot3\cdot5\cdot67.\]

Thus, since $6+7 = 13$, $\boxed{\textbf{(E)}~13}$ is the answer.

~pineconee

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