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 <math>2016</math>?
+
What is the sum of the distinct prime integer divisors of 735
 +
?
  
 
<math>\textbf{(A) }9\qquad\textbf{(B) }12\qquad\textbf{(C) }16\qquad\textbf{(D) }49\qquad \textbf{(E) }63</math>
 
<math>\textbf{(A) }9\qquad\textbf{(B) }12\qquad\textbf{(C) }16\qquad\textbf{(D) }49\qquad \textbf{(E) }63</math>

Revision as of 23:56, 27 May 2024

Problem

What is the sum of the distinct prime integer divisors of 735 ?

$\textbf{(A) }9\qquad\textbf{(B) }12\qquad\textbf{(C) }16\qquad\textbf{(D) }49\qquad \textbf{(E) }63$

Solutions

Solution 1

The prime factorization is $2016=2^5\times3^2\times7$. Since the problem is only asking us for the distinct prime factors, we have $2,3,7$. Their desired sum is then $\boxed{\textbf{(B) }12}$.

Video Solution (CREATIVE THINKING!!!)

https://youtu.be/GNFnta9MF9E

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Video Solution

https://youtu.be/1KN7OTG3k-0

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See Also

2016 AMC 8 (ProblemsAnswer KeyResources)
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

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