How do you know when you've found all the factors for a number?

Answer 1

If you know the prime factorization of a number, you can find out the total number of factors.
Example: 210
21 x 31 x 51 x 71 = 210
Add one to the exponents and multiply them.
2 x 2 x 2 x 2 = 16, the total number of factors.
You know that 1, 2, 3, 5, and 7 are factors. You need three more to get halfway.
2 x 3 = 6
2 x 5 = 10
2 x 7 = 14
Divide all those numbers into 210.
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

You know you've found all the factors of a number when the next first factor exceeds its corresponding second factor. For example, after you found that 4 was a factor of 24 and 5 was not, you would see that 6, the next factor of 24, had already been included in a pair of factors. Thus, all the factors have been found.

Answer 2

There is no simple way to find the answer to the question in general. The question needs to be more specific.

Answer 3

Every number is both a factor and a multiple of itself. Every other factor is smaller than the number, every other multiple is larger than the number.

Answer 4

Use multiples when you're adding or subtracting them.

Use factors when you're reducing them.