Factoring Made Easy

Factoring a natural number involves breaking it down into its prime divisors or factors. There are a few factors that are easy to determine: 2, 3, 5, and 11. All even numbers are divisible by 2, like 26 or 112, all even numbers can be divided by 2, so 2 will be a factor of anything even.

For 3, if the digits of the number sum to a multiple of 3, it is also divisible by 3, like 258, 2 plus 5, plus 8. 2 plus 8 is 10, 10 plus 5 is 15, since 15 is a multiple of 3, then 258 can be divided by 3, thus 3 is a factor of 258. For 5, any number that ends in 5 or 0 is divisible by 5.

For instance, 20 is divisible by 5, 35 is divisible by 5, 1,260 is divisible by 5, etc. As long as it ends in a 0 or a 5 it’s divisible by 5 or has 5 as a factor. Now 11, 11 is a special one. Let’s take for instance the number 1,023.

1,023 is divisible by 11 because when you add the odd digits together, so the first and the third digits, you get 3, when you add the even digits together, 0 and 3, you get 3.

When you subtract the sum of the odd digits minus the sum of the even digits you get 0. As long as when you subtract the sum of the odd digits minus the sum of the even digits and get 0 or a multiple of 11, then that number is divisible by 11, or 11 is a factor of that number.