If a number ends in the digit 2, 4, 6, 8 or 0, it is divisible by 2. To start factoring, write the number and draw two lines under it, one going down and to the left, the other going down and to the right. Below the left-hand line, write "2." Below the right-hand line, write the result of dividing the original number by 2. For example, if you are factoring 168, you should have 2 and 84 beneath it. Circle the 2, because it's prime, and repeat the process with the 84. You're building a factor tree, and you should end up with three 2's and a 21.
No matter how large or small the number, there's a simple test to see if a number is evenly divisible by 3: add up the digits. If the sum is evenly divisible by 3, then so is the larger number. In the example from Section 1, 21 is no longer divisible by 2. However, adding up the digits for 21 = 2+1 = 3. You can divide 3 evenly by itself, so 21 is divisible by 3. Simple testing leads to the result of 7x3. Circle the 3, because you can't divide 3 evenly by anything but itself and 1. Now, you're done with the factoring of 168. Its prime factors are 2x2x2x3x7; the composite factors are any combination of two or more of the prime factors.
If a number is divisible by 5, it will end with a "5" or a "0." None of the numbers in this example are divisible by five, but in other cases, five is a prime factor that you can pull out.
There are ways to test very large numbers for divisibility by 7 or 11. You're going to end up with a faster solution by using a calculator, but the tests are available at the third link under "References." Both of these tests have many steps, but they will give you tools to break down numbers into prime and composite factors.