thegame12 wrote:

Thank you!

It depends on how big the number is!

If it's a small number, you can create a factor table and just write out all of the factors. They come in pairs, and the table will look like this:

241 x 24

2 x 12

3 x 8

4 x 6

Start with 1 (which is a factor of every integer), and move upwards until you've got all of them. 24 has 8 factors in total. You know you have all of them when moving upwards would give you a factor (in this case, 6) that you already found.

If the number is too big to do this, you can start with the prime factors and figure it out from there. Suppose we're trying to figure out how many factors 2,400 has.

Prime factorization of 2,400 = 2*2*2*2*2*3*5*5

That's five 2s, one 3, and two 5s.

By definition, every factor of 2400 will be made up of some combination of those prime factors. For instance, 2*2*2 is a factor of 2400. So is 2*3*5*5. But 2*3*7 isn't, because it has a 7 in it, and there's no 7 in 2400.

How many ways can you combine those prime factors?

You can use anywhere from zero to all five of the 2s - that's 6 possibilities...

you can either use the 3 or not use it - that's 2 possibilities...

you can use zero, one, or two of the 5s - that's 3 more possibilities.

6*2*3 = 36 factors in total.

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