A collection of potential factors
A factor of a number will divide into the original number evenly. Factorization usually means finding all of the prime numbers that are factors. A prime number is a number that cannot be factored any further (other than saying 1 times the number itself). You may be required to factor numbers in middle school, high school or even college. You also may have to perform this task as a part of math- or science-related career fields.
Instructions
1. Look for numbers that end in zero or five. These numbers are divisible by five, which is a prime number. For instance, the number 25 is divisible by five. You could list the factorization as "5, 5," or "5^2" (5 squared).
2. Look for even numbers, which means that they are divisible by two. For instance, you would factor the number 26 by dividing two into it, leaving the number 13. Therefore, the factors of 26 are "2, 13."
3. Look for numbers whose digits add up to a number that is divisible by the number three. For instance, if you add the one and the five in the number 15, you get an answer of six. This means that the number is divisible by three. Therefore, 15 would be factored as "3, 5." This is especially helpful as a beginning step for factoring larger numbers.
4. Work your way downward using the previous steps when factoring a larger number. For instance, if you have the number 200, you know that you could start with five or two because it ends in a zero and is an even number. You also can rule out three as a factor because the sum of the digits does not equal a number that is divisible by three. So if you start with five (one of your factors), this number divides into 200 40 times. Forty is not a prime number, so you must break it down further. Because it is divisible by five as well, you can conclude that 200 has the factors of "5, 5 and 8." The number eight can be further broken into three two's. Therefore, the factorization of 200 would be "5, 5, 2, 2 and 2," or "5^2, 2^3" (five squared and two cubed).
Tags: divisible five, number that, prime number, divisible three, factor number, factoring larger