How do you know when you have found all the factors of a number?

Write the number in terms of its prime factors. So suppose is is:

Z = ap*bq*cr ...

where a, b, c are prime factors and p, q, r are indices.

Then the total number of factors of Z is (p+1)*(q+1)*(r+1) ...

If you have fewer, you have missed some out.

Alternatively,

Test Z for divisibility by each integer, from 1 upwards to sqrt(Z). At each stage, make a note of any factor found as well as the quotient when it divides Z.

If you are thorough, you will find all the factors. This method may be simpler but relies absolutely on systematically going through many integers as potential divisors.