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
, so the answer is
.
Solution by greersc.
See Also
2019 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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