EDGE Math 8

Factoring Numbers

To factor a natural number means to express it as a product of two other natural numbers.

For example, 18 can be expressed as $18 = 1 \cdot 18,$ $18 = 2 \cdot 9,$ $18 = 3 \cdot 6.$ The numbers 1, 2, 3, 6, 9, and 18 are called the factors of 18. Recall that a natural number that is not equal to 1 is a prime number if it has no factor other than 1 and itself. For example, 2 and 3 are prime numbers, while 4 is not.

Every natural number that is not equal to 1 can either be a prime number or be expressed as a product of prime numbers. For example:

2 is a prime number;
3 is prime number;
4 is a product of prime numbers, since

4 = 2 \cdot 2;

5 is a prime number;
6 is a product of prime numbers, since

6 = 2 \cdot 3;

7 is a prime number;
8 is a product of prime numbers, since

8 = 2 \cdot 2 \cdot 2;

9 is a product of prime numbers, since

9 = 3 \cdot 3;

and
10 is a product of prime numbers, since

10 = 2 \cdot 5;

and
11 is a prime number.