We see that the odd factors are 3^4, 5^2 and 7^1. I have two issues here:

Why is he multiplying 5X3X2 when the question asks “how MANY”? Shouldn’t be 5+3+2?

He says 3^0, 5^0, 7^0 should still be counted as odd factors. Why? He gives the example of “if you have 3 jeans, 2 pairs of socks, 3 shirts how many outfits can you make”? Well…why arent you making the 3 jeans into 3^0 jeans then?

Let’s create an easier example. If you have 6! the odd factors are 5^1, 3^2. If you add them together, the result will be (2+3) - 5 such odd factors. However if you multiply them, the result would be 2*3 = 6.

If you want a more math explanation. For 3^2 you have 3 choices (zero 3s, one 3, two 3s), same goes for 5 (zero 5s, one 5). So like Leaderboard says, it comes down to the choice method.