1993 AJHSME Problems/Problem 3

Problem

Which of the following numbers has the largest prime factor?

$\text{(A)}\ 39\qquad\text{(B)}\ 51\qquad\text{(C)}\ 77\qquad\text{(D)}\ 91\qquad\text{(E)}\ 121$

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 $\boxed{B}$