To find the numbers, you can start with any factor pair of the number and keep factoring the composite numbers until all factors are prime.
315
3 x 105
3 x 3 x 35
3 x 3 x 5 x 7 = 315
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2 and 17
525 = 3*5*5*7
3 x 3 x 3 x 11 = 297
There are no two prime numbers in which a product of 100 is possible.
It only takes three. 5 x 5 x 7 = 175