Here is the question below and the screenshot is from Greg’s explanation of the solution! This is possibly the first video where I am not understanding anything he is saying. He is calling out some factor trick and I have no idea what it is!

Already thanks!

Thank you really, but I am kind of short on time to go through all videos so I am picking them on a need basis and there is no video with the name factor trick!

It would be really really helpful if you could just directly share the link after opening which video! Sorry! Thanks!

Just look at the videos *related* to factors (i.e, with the Factor title).

Total factors include negative factors.

A number with three distinct prime divisors (2, 3, and 5, for example) has at least 8 positive factors, or 16 total factors. This is the case for the number 2 * 3 * 5 (30).

I try to increase the number of factors by as little as possible (while still having 2,3, and 5) by multiplying 30 by 2. Prime factorization becomes 2^2 * 3^1 * 5^1, which has 3 * 2 * 2 = 12 positive factors, or 24 total factors. Because I increased this total # of factors as little as possible, and I passed 20, I reason that I can’t have a number with 20 total factors that satisfies the constraints, and I choose A.

Another way to do this is to think/calculate in factors, rather than the actual numbers. I recognize that with three distinct prime divisors, I know that I need to multiply three numbers that are greater than 1 together (the exponents of the primes + 1) to get all of the positive factors. Then I multiply by 2 to get all factors. This is to say: the incorrect answer choice can NOT be made by multiplying three numbers greater than 2 together, then multiplying again by 2.

**answer for number of factors**

20: cannot satisfy the above requirements (2 * 2 * 5)

24: 2 * 2 * 2 * 3

36: 2 * 2 * 3 * 3

48: 2 * 2 * 3 * 4

54: 2 * 3 * 3 * 3