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

(Created page with '==Problem== Which of the following numbers has the largest prime factor? <math> \text{(A)}\ 39\qquad\text{(B)}\ 51\qquad\text{(C)}\ 77\qquad\text{(D)}\ 91\qquad\text{(E)}\ 121 <…')
 
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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>.
 
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>.
  
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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>.
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C. The prime factor of <math>77</math> are <math>7</math> and <math>11</math>. Therefore, the largest prime factor is <math>11</math>.
  
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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>.  
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D. The prime factor of <math>91</math> are <math>7</math> and <math>13</math>. Therefore, the largest prime factor is <math>13</math>.
  
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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.  
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E. The prime factor of <math>121</math> are <math>11</math>. Therefore, the largest prime factor is <math>11</math>.
  
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Since we are looking for the number with the largest prime factor, the correct answer would be <math>\boxed{B}</math>
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So, the answer is <math>B</math>
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==See Also==
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{{AJHSME box|year=1993|num-b=2|num-a=4}}
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{{MAA Notice}}

Latest revision as of 13:27, 27 November 2022

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 factor of $77$ are $7$ and $11$. Therefore, the largest prime factor is $11$.

D. The prime factor of $91$ are $7$ and $13$. Therefore, the largest prime factor is $13$.

E. The prime factor of $121$ are $11$. Therefore, the largest prime factor is $11$.

So, the answer is $B$

See Also

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

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