Difference between revisions of "2022 AMC 8 Problems/Problem 3"
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Revision as of 01:12, 20 January 2023
Contents
Problem
When three positive integers , , and are multiplied together, their product is . Suppose . In how many ways can the numbers be chosen?
Solution 1
The positive divisors of are It is clear that so we apply casework to
- If then
- If then
- If then
- If then
Together, the numbers and can be chosen in ways.
~MRENTHUSIASM
Solution 2
The positive divisors of are We can do casework on :
If , then there are cases:
If , then there is only case:
In total, there are ways to choose distinct positive integer values of .
~MathFun1000
Video Solution 1
https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=142
Video Solution 2
Video Solution
https://youtu.be/Q0R6dnIO95Y?t=98
See Also
2022 AMC 8 (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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.