2019 AMC 10B Problems/Problem 19
Problem
Let be the set of all positive integer divisors of How many numbers are the product of two distinct elements of
Solution
To find the number of numbers that are the product of two distinct elements of , we first square and factor it. Factoring, we find . Therefore, has distinct factors. Each of these can be achieved by multiplying two factors of . However, the factors must be distinct, so we eliminate and , which is , so the answer is .
Solution by greersc. (Edited by AZAZ12345 and then by greersc once again)
See Also
2019 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.