Difference between revisions of "2016 AMC 8 Problems/Problem 9"
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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 <math>2016</math>? | ||
Revision as of 03:49, 16 January 2021
Problem
What is the sum of the distinct prime integer divisors of ?
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 .
Solution 2
We notice that , since , and . We can divide by to get . This is divisible by , as . Dividing by , we have . This is clearly divisible by , leaving . We have . We know that and are both multiples of , is , and is prime. This means that the distinct prime factors are and . Their sum is .
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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All AJHSME/AMC 8 Problems and Solutions |
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