A factor is a whole number that fits evenly into another whole number. For example, 3 is a factor of 9, because you can fit 3 evenly three times into 9: 3 x 3 = 9.
Four is not a factor of 9, because there is no way to fit fours evenly into 9: 4 x 2 = 8, leaving one left over, and 4 x 3 = 12, which is three too many.
To find all the factors of a number, you need to check all of the smaller numbers to see whether they fit evenly into that number. There isn't a system or a trick to do it. On the other hand, you can certainly eliminate some choices - if you know that 2 isn't a factor of 27, then you can see that no multiples of 2 will be factors of 27. So you don't have to try any even number. If a number ends in 0 or 5, then five is one of its factors, but if it doesn't, then five is not one of its factors.
Some numbers have no factors other than one and themselves. We call these numbers prime numbers. For example, 1, 3, 5, 7, and 11 are all prime numbers. Larger numbers can be prime too: 47 is prime, and 997 is also prime.
To find out more about numbers, check out these books from Amazon.com or from your library: