#1**+2 **

factor(840) = ((2^3*3)*5)*7 = (2^3) *3*5*7

so there are 6 prime factors (2 occurs 3 times)

I can have 3,5,7 and some of the 2s (1,2,or 3 twos)

3 ways

I can have two of 3,5,7 and 2 or more number of 2s (2 or 3 twos)

3C2*2 = 6 ways

I can have one of 3,5,7 and all 3 twos

3*1 = 3 ways

3+6+3 = 12 ways

So I think there are 12 factors of 840 that have at least 4 factors.

Melody Mar 21, 2019