Difference between revisions of "2016 AMC 8 Problems/Problem 9"
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== Problem == | == Problem == | ||
| − | What is the sum of the distinct prime integer divisors of | + | What is the sum of the distinct prime integer divisors of <math>2016</math>? |
| − | ? | ||
| − | <math>\textbf{(A) }9\qquad\textbf{(B) } | + | <math>\textbf{(A) }9\qquad\textbf{(B) }12\qquad\textbf{(C) }16\qquad\textbf{(D) }49\qquad \textbf{(E) }63</math> |
==Solutions== | ==Solutions== | ||
| Line 10: | Line 9: | ||
===Solution 1=== | ===Solution 1=== | ||
| − | The prime factorization is <math> | + | The prime factorization is <math>2016=2^5\times3^2\times7</math>. Since the problem is only asking us for the distinct prime factors, we have <math>2,3,7</math>. Their desired sum is then <math>\boxed{\textbf{(B) }12}</math>. |
| + | |||
| + | ==Video Solution== | ||
| + | |||
| + | https://youtu.be/I_jevKp3Kyg?si=qKDYbUmjFkioeIvE | ||
| + | |||
| + | ~Elijahman~ | ||
==Video Solution (CREATIVE THINKING!!!)== | ==Video Solution (CREATIVE THINKING!!!)== | ||
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~Education, the Study of Everything | ~Education, the Study of Everything | ||
| − | |||
==Video Solution== | ==Video Solution== | ||
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{{AMC8 box|year=2016|num-b=8|num-a=10}} | {{AMC8 box|year=2016|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
| + | [[Category:Introductory Number Theory Problems]] | ||
Latest revision as of 18:04, 25 June 2025
Contents
Problem
What is the sum of the distinct prime integer divisors of 
?
Solutions
Solution 1
The prime factorization is 
. Since the problem is only asking us for the distinct prime factors, we have 
. Their desired sum is then 
.
Video Solution
https://youtu.be/I_jevKp3Kyg?si=qKDYbUmjFkioeIvE
~Elijahman~
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
| 2016 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
