Problem 553

The number 315 can be written as the product of two odd integers each greater than 1 . In how many ways can this be done?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 5

## Solution

Factoring 315 into primes, we find that $315=3 \times 3 \times 5 \times 7$.

The factorization of 315 as the product of 2 odd integers is $3 \times 105,5 \times 63,7 \times 45,9 \times 35$, and $15 \times 21$. There are 5 possible factorizations.