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

Revision as of 11:20, 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
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All AJHSME/AMC 8 Problems and Solutions

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 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==