# 1993 AJHSME Problems/Problem 3

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## Problem

Which of the following numbers has the largest prime factor? $\text{(A)}\ 39\qquad\text{(B)}\ 51\qquad\text{(C)}\ 77\qquad\text{(D)}\ 91\qquad\text{(E)}\ 121$

## Solution

A. The prime factors of $39$ are $3$ and $13$. Therefore, the largest prime factor is $13$.

B. The prime factors of $51$ are $3$ and $17$. Therefore, the largest prime factor is $17$.

C. The prime factors of $77$ are $7$ and $11$. Therefore, the largest prime factor is $11$.

D. The prime factors of $91$ are $7$ and $13$. Therefore, the largest prime factor is $13$.

E. The only prime factor of $121$ is $11$. This makes $11$ the largest prime factor of this number.

Since we are looking for the number with the largest prime factor, the correct answer would be $\boxed{\text{(B)}}$.

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 