Factorization

A factor is simply a number that is multiplied to get a product. Factoring a number means taking the number apart to find its factors--it's like multiplying in reverse. Here are lists of all the factors of 16, 20, and 45.

16 --> 1, 2, 4, 8, 16
20 --> 1, 2, 4, 5, 10, 20
45 --> 1, 3, 5, 9, 15, 45
12 --> 12, 24, 36, 48, 60, . . .
5 --> 5, 10, 15, 20, 25, . . .
7 --> 7, 14, 21, 28, 35, . . .

Factors are either composite numbers or prime numbers. A prime number has only two factors, one and itself, so it cannot be divided evenly by any other numbers. Here's a list of prime numbers up to 100. You can see that none of these numbers can be factored any further.

PRIME NUMBERS to 100

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

A composite number is any number that has more than two factors. Here's a list of composite numbers up to 20. You can see that they can all be factored further. For example, 4 equals 2 times 2, 6 equals 3 times 2, 8 equals 4 times 2, and so forth.
By the way, zero and one are considered neither prime nor composite numbers-they're in a class by themselves!

COMPOSITE NUMBERS up to 20

4,6,8,9,10,12,14,15,16,18,20

You can write any composite number as a product of prime factors. This is called prime factorization. To find the prime factors of a number, you divide the number by the smallest possible prime number and work up the list of prime numbers until the result is itself a prime number. Let's use this method to find the prime factors of 168. Since 168 is even, we start by dividing it by the smallest prime number, 2. 168 divided by 2 is 84.
84 divided by 2 is 42. 42 divided by 2 is 21. Since 21 is not divisible by 2, we try dividing by 3, the next biggest prime number. We find that 21 divided by 3 equals 7, and 7 is a prime number. We know 168 is now fully factored. We simply list the divisors to write the factors of 168.

168 ÷ 2 = 84
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7 Prime number
prime factors = 2 × 2 × 2 × 3 × 7

To check the answer, multiply these factors and make sure they equal 168.
Here are the prime factors of the composite numbers between 1 and 20.

4 = 2 × 2
6 = 3 × 2
8 = 2 × 2 × 2
9 = 3 × 3
10 = 5 × 2
12 = 3 × 2 × 2
14 = 7 × 2
15 = 5 × 3
16 = 2 × 2 × 2 × 2
18 = 3 × 3 × 2
20 = 5 × 2 × 2

Factorization