Problem:
When three positive integers and are multiplied together, their product is . Suppose . In how many ways can the numbers be chosen?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The factors of are , , , , , , , , and . Consider each possible value of a and determine whether there are any solutions given that = 100 and .
If , then = 100. There are solutions: , , and .
If , then . There is solution: .
If , then . There are no solutions given that .
In summary, there are 4 ways to choose the numbers , , and :
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions