Answer: 3^32 * 2^2
= 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 2 * 2
= 7,412,080,755,407,364
and 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 2 + 2 = 100.
Since 1 would not be a factor, and any 4 could be replaced by two 2's without decreasing the product. If one of the factors, n, was greater than 4, replacing it with 2 and (n - 2) would yield a larger product. So the factors are all 2's and 3's.
