Factoring
Overview: Factoring Numbers
When you factor a number, you break it apart to find the integers that can be multiplied together to produce the original number.
Factor the number 30
30 = (1)(30)
30 = (2)(15)
30 = (3)(10)
30 = (5)(6)
1,2,3,5,6,10,15,30 are all factors of 30.
Factors can be composite numbers or prime numbers.
A composite number is any number that has more than two factors.
In the example above, 15, 10, and 6 are composite numbers. They can be broken down further.
15 = (3)(5)
10 = (2)(5)
6 = (2)(3)
A prime number is a positive number greater than 1 that has exactly two divisors: 1 and itself.
The first 30 primes:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67,
71, 73, 79, 83, 89, 97, 101, 103,
107, 109, 113
(0 and 1 are not considered prime or composite.)
Prime Factorization
To find the prime factors of a number:
- Divide the number by the smallest possible prime number.
- Divide the result by the smallest possible prime number.
- Continue until the result is also a prime number.
Find the prime factorization of 30
30 ÷ 2 = 15
15 ÷ 3 = 5
2,3,5 are the prime factors of 30.
Check your answer: (2)(3)(5) = 30
When you multiply all of the prime factors of a number,
the product (result) is the original number.
Find the prime factorization of 168
168 ÷ 2 = 84
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
2,2,2,3,7 are the prime factors of 168.
Check your answer: (2)(2)(2)(3)(7) = 168
Factoring is useful in algebra for simplifying expressions and solving equations.