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

Revision as of 12:20, 28 March 2021

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 $17$ .

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 8: / Line 8: @@
 B. The prime factors of <math>51</math> are <math>3</math> and <math>17</math>. Therefore, the largest prime factor is <math>17</math>.
-C. The prime factors of <math>77</math> are <math>7</math> and <math>11</math>. Therefore, the largest prime factor is <math>11</math>.
-D. The prime factors of <math>91</math> are <math>7</math> and <math>13</math>. Therefore, the largest prime factor is <math>13</math>.
-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{\text{(B)}}</math>.
 ==See Also==