Though I rarely need to know the factors of a number, using Prime Factors to find all of the factors of a number is handy when the number is very large. We will start with a small one...48.

The prime factorization of 48 is
6 * 8
3*2*2*2*2.

Here is how I use 3*2*2*2*2 to find all of the factors of 48.
First all numbers have 1 as a factor.
Next, I see a 2.
Do you see a 2?

3*2*2*2*2.......{1, 2

Now, I see 3
and just as easily 2*2=4.

3*2*2*2*2.......{1, 2, 3, 4

5 is not shown and can't be made - but 6 is there! (3*2=6)

3*2*2*2*2.......{1, 2, 3, 4, 6

There are no sevens, but 2*2*2 is 8

3*2*2*2*2.......{1, 2, 3, 4, 6, 8

A pair of threes would give me nine, but I only have 1.
I won't look for 10 since 5 isn't a factor.
11 was eliminated during the prime factoring.
12 is there (3*2*2)
and 16 is there (2*2*2*2)

3*2*2*2*2.......{1, 2, 3, 4, 6, 8, 12, 16,

Now I just need to finish the combinations. (3*2*2*2 = 24 and 3*2*2*2*2=48)

The factors of 48 are ....... 3*2*2*2*2 ....... {1, 2, 3, 4, 6, 8, 12, 16, 24, 48)

The factors of 100 are ....... 5*5*2*2
The combinations are (2), (2*2), (5), (2*5), (2*2*5), (5*5), (5*5*2) and (5*5*2*2)
The factors are .. {1, 2, 4, 5, 10, 20, 25, 50, 100}