2005 AMC 12B Problems/Problem 21
Problem
A positive integer has divisors and has divisors. What is the greatest integer such that divides ?
Solution
We may let , where is not divisible by 7. Using the fact that the number of divisors function is multiplicative, we have . Also, . These numbers are in the ratio 3:4, so .
See also
2005 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 20 |
Followed by Problem 22 |
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 AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.