1. Factors

2. What is a Factor?
If a number 𝑎 divides evenly (with no remainder) into another number 𝑏, then it is said that 𝑎 is a factor of 𝑏.

3. What is a Factor?
If a number 𝑎 divides evenly (with no remainder) into another number 𝑏, then it is said that 𝑎 is a factor of 𝑏. In this way, 4 is a factor of 12.

4. Examples
List all the factors of 12:

5. Examples
List all the factors of 12: 1, 2, 3, 4, 6, 12

6. Examples
List all the factors of 12: 1, 2, 3, 4, 6, 12 List all the factors of 32:

7. Examples
List all the factors of 12: 1, 2, 3, 4, 6, 12 List all the factors of 32: 1, 2, 4, 8, 16, 32

8. Examples
List all the factors of 12: 1, 2, 3, 4, 6, 12 List all the factors of 32: 1, 2, 4, 8, 16, 32 Notice that 1 and the number itself are always in the list of factors!

9. Examples
List all the factors of 12: 1, 2, 3, 4, 6, 12 Some numbers are in both List all the factors of 32: lists 1, 2, 4, 8, 16, 32

10. Examples
List all the factors of 12: 1, 2, 3, 4, 6, 12 Some numbers are in both List all the factors of 32: lists 1, 2, 4, 8, 16, 32 These are the common factors of 12 and 32.

11. Highest Common Factor
The lowest common factor for any pair of numbers is always 1, so this is not very interesting and of little use. The HCF on the other hand will come in very useful later in mathematics. HCF(12,32)=4