Factoring made easy

Prime numbers are numbers (besides 1 and 0) which can only be divided completely by 1 and itself. Examples of prime numbers are 2, 3, 5, 7, etc. Any number can be written as the product of prime numbers. This is called prime factoring. Learning how to factor a number down to its primes can really be helpful when working with fractions. Factoring can be helpful when finding least common multiple and reducing large fraction products. Let's get started.

The trick is often to know where to get started. Here are few simple rules to make it easier on you.

1. Keep track of your prime numbers as you pull them out. Don't lose any! Maybe write them down somewhere.
2. Find the approximate square root of the number. You will only need to check to see if a prime number is a factor if it is less than or equal to that square root.
3. Is the number prime? Then you are finished.
4. Is the number even? Then it is divisible by 2. This takes care of half the numbers.
5. Does the number end in 5 or 0? Then it is divisible by 5.
6. Add the integers in the number up. If the sum is bigger than 9 then add the integers in the sum until the result is less than or equal to 9. Is the sum equal to 3, 6 or 9? Then the number is divisible by 3.
7. After 2, 3 and 5, take the next biggest prime number and see if it divides evenly. Remember to keep checking until you reach the square root.
8. Take the remainder and start over with it until the remainder is prime.

Let's try an example: Factor 102.

• What is the approximate square root of 102? The square root of 100 is 10, so 10 is approximate. We only have to check up to 10.
• Is 102 prime? No. Is 102 even? Yes, then divide by 2. 102 / 2 = 51
• What is the approximate square root of 51? The square root of 49 is 7, so 7 is the approximate square root.
• Is 51 a prime number? I'm not sure. Is 51 even? No. D0es 51 end in 5 or 0? No. Does 5+1 add up to 3, 6 or 9? Yes, then divide by 3. 51 / 3 = 17.
• What is the approximate square root of 17? 17 is close to 16 so the approximate square root is 4.
• Is 17 prime? Yes, then we are done. 102 = 2 * 3 * 17.

Good Luck and remember that factoring can be your friend.