Factoring


"Factoring" involves finding the numbers or "factors" you multiply to get another number. For instance, the factors of 15 are 3 and 5, because 3x5=15. Some numbers have more than one factorization (way of being factored). For instance, 12 can be factored as 1x12, 2x6, or 3x4. A number that can be only factored as 1 times itself is called "prime". The first few primes are 2,3,5,7,11,13. The number 1 is not regarded as a prime, and is usually not included in factorizations because 1 goes in to everything.







You most often want to find the "prime factorization" of a number. That is, you usually want to find the list of all the prime-number factors of a given number. The prime factorization does not include 1, but does include every copy of every prime factor. For instance, the prime factorization of 8 is 2x2x2, not just "2".

There are at least 2 ways that you can find the prime factors of a number or an expression.



Method

Explanation

1. Finding the prime factorization of 24.
Picture_5.png
Going from top to bottom,
Divide 24 by 2 = 12
Divide 12 by 2 = 6
Divide 6 by 2 = 3
So the prime factorization of
24 is 2 x 2 x 2 x 3
2. Finding the prime factorization of x² - 4x -5.
work.png
In order to factor x² -4x - 5, you can use a 4-box.
The four individual squares must add up to x² -4x - 5.
The length and width of the box will be our factors.



Further Discussion

  • Is factoring really this easy?
  • When is factoring helpful?