What number under one million has the most factors?

Question

What number <1,000,000 has the most factors?

I know that if the prime factorization of N is
(2^a)(3^b)(5^c)(7^d).... then the formula
(a+1)(b+1)(c+1)(d+1)..... give the total number of factors that N has. But without testing every number up to one million, how can you find the one with the most factors and prove that it has the most?

Answer 1

720,720

It has 240 factors