Difference between revisions of "1993 AJHSME Problems/Problem 3"

Revision as of 22:25, 22 December 2012

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

1993 AJHSME (Problems • Answer Key • Resources)
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

@@ Line 15: / Line 15: @@
 E. The only prime factor of <math>121</math> is <math>11</math>. This makes <math>11</math> the largest prime factor of this number.
-Since we are looking for the number with the largest prime factor, the correct answer would be <math>\boxed{B}</math>
+Since we are looking for the number with the largest prime factor, the correct answer would be <math>\boxed{\text{(B)}}</math>.
+==See Also==
+{{AJHSME box|year=1993|num-b=2|num-a=4}}