Be extremely systematic. I make couples, starting with one, and counting up. You'll soon cover everything:
60:
1&60
2&30
3&20
4&15
5&12
6&10
By counting up on the low end, you cover everything on the high end as well. In this example, the next factor up from 6 is 10, and that's already there, and so is everything else above 10. This is better than randomly throwing out numbers until you hit them all.
Try it with a couple of examples that have lots of factors, like 24, 72, 36, 105.
Try it also with some variables: Name all the factors of 4p if p is a prime number.
4p:
1&4p
2&2p
4&p
That's it!