What Does Factoring Mean?
In math, factoring is a process that involves breaking a composite number down into its components. A composite number is one that has more factors than 1 and itself.
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Steps
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To factor a number, begin by breaking the composite number up into two factors. For example, if you were factoring the number 36 you could break it up into 4 X 9. Continue to do this until you have only prime numbers remaining.
Prime Numbers
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Prime numbers are numbers that have no factors besides the number itself and the number 1. For example, 13 is a prime number because it can only be divided evenly by 13 and 1.
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Factor Notation
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Once you have only prime numbers left, you are finished factoring. Write your final answer as all of the factors multiplied by each other. If there are repeats of a factor, use exponents. For example, the notation for 36 would be 3^2 X 2^2
Divisibility Rules
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Divisibility rules help you identify what factors a number might be divisible by. For example, if the number is even, it is divisible by two. If the sum of the digits in a number add up to a number that is divisible by three, the number will be divisible by three.
Algebraic Factoring
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Factoring can also be used for algebraic expressions involving variables. For example, x^2 - 9 could be factored into (x - 3)(x + 3).
Uses
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Factoring can be used to simplify and solve equations. For example, if you had to solve x^2 - 9 = 0, you would factor it to (x - 3)(x + 3) = 0 and find that x must be positive 3 or negative 3. You can also use factoring to determine how a larger group can be split into smaller, equal-sized groups. For example, a group of 20 people could be split into 2 teams of 10, 4 teams of 5, 5 teams of 4 or 10 teams of 2.
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