Difference between revisions of "2009 CEMC Gauss (Grade 8) Problems/Problem 21"
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Latest revision as of 21:37, 19 October 2025
Problem
The product of four different positive integers is . What is the maximum possible sum of these four integers?
Solution
We want to make the first three integers the smallest that they can be, but make the fourth integer as large as it can be. However, since the integers are distinct, we cannot just make three of them and the last
.
We can find the prime factorization of , which is
.
We can now see that the three smallest integers are ,
, and
, which multiply to
. This means the last number must be
.
Summing all of our numbers together, we get
~anabel.disher
2009 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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CEMC Gauss (Grade 8) |