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 $\boxed{\text{(B)}}$.

See Also

1993 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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