What Is Factoring in Math?

Factorization is an essential part of mathematics.

Factoring--or factorization--is the process through which mathematicians and others take a number and break it into all of the whole numbers into which it can be divided, which are called "factors." It is a fundamental operation of algebra, trigonometry, and calculus, and most students begin to learn it at the junior high level.

Features

A "prime" number is a whole number that cannot divide into any whole number other than 1 (or -1) and itself, such as 1, -3, and 17. A "composite" number is a number that can be divided into other whole numbers, such as 16 and -128. In factorization, you take the source number, which is a composite number, and break it into all of the prime numbers into which it is divisible. All numbers into which the original composite number is divisible--even other composite numbers--are its factors.

Function

The most basic method of factorization is the factor tree method. To perform a factor tree operation, write the original composite number, and then draw two lines raying off from it. At the end of the first line, write the smallest prime number into which it is divisible, such as 2, 3 or 5. Divide the original number by that number, and write the quotient at the end of the other line. If the quotient is another composite number, draw two lines raying off from it, and repeat these steps until the number at the end of every line is a prime number.

Types

The type of factorization illustrated above is only for single numbers. In cases where you are dealing with polynomials and quadratic equations in linear algebra and higher levels of math, you need to use more complicated methods to find the factors. For example, the factors of the expression x^2-10x-24 are (x+2)(x-12).

Benefits

Factorization generally allows you to break large composite numbers and complicated expressions into workable units that integrate neatly into other operations. These "workable units" are also known as divisors.

Potential

In disciplines that use high levels of mathematics, such as physics and engineering, factorization becomes a key aspect of many operations. In these disciplines, you deal with the factors of polynomial expressions as a completely separate "set" of numbers, just as real numbers, rational numbers, and natural numbers are all "sets."

References

• University of Illinois: The Quadratic Sieve Factoring Algorithm
• Purplemath: Simple Polynomial Factoring

Resources

• Alpertron: Polynomial Factorization Applet