# Greatest Common Factor

### What is factor?

Factors are numbers that you multiply together to get another number.

For example, 2 X 9 = 18, so 2 and 9 are factors of 18.

A number can have multiple factors.

For example, factors of 16 are 1, 2, 4, 8, 16.

Because 1 x 16 = 16

2 x 8 = 16

4 x 4 = 16

### What is common factor?

If the factors of two or more numbers are similar, it is called common factor.

For example, the common factors of 12, 18, 30.

Factors of 12 are 1, 2, 3, 4, 6, and 12

Factors of 18 are 1, 2, 3, 6, 9, and 18

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30

You can notice that the numbers 1, 2, 3, and 6 are appearing in all of the lists. So, the common factors of 12, 18, and 30 are 1, 2, 3, 5, and 6.

### What is the greatest common factor?

Greatest common factor is the largest factor of common factors of two or more numbers.

As you have seen in the previous example, the common factors of 12, 18, and 30 are 1, 2, 3, 5, and 6. So the Greatest Common Factor of 12, 18, and 30 is 6.

### How to find the greatest common factor?

### More GCF examples

**Greatest common factor of 8 and 12**

Factors of 8 = 1, 2, 4, 8

Factors of 12 = 1, 2, 3, 4, 6, 12

Common factors of 8 and 12 = 1, 2, 4**GCF of 8 and 12 = 4**

**Greatest common factor of 28 and 36**

Factors of 28 = 1, 2, 4, 7, 14 and 28

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36

Common factors of 28 and 36 = 1, 2, 4,**GCF of 28 and 36 = 4**

**Greatest common factor of 45 and 75**

Factors of 45 = 1, 3, 5, 9, 15 and 45

Factors of 75 = 1, 3, 5, 15, 25, and 75

Common factors of 45 and 75 = 1, 3, 5, 15**GCF of 45 and 75 = 15**

**Greatest common factor of 3 and 9**

Factors of 3 = 1, 3

Factors of 9 = 1, 3, and 9

Common factors of 3 and 9 = 1, 3**GCF of 3 and 9 = 3**

**Greatest common factor of 24 and 32**

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24

Factors of 32 = 1, 2, 4, 8, 16, and 32

Common factors of 24 and 32 = 1, 2, 4, and 8**GCF of 24 and 32 = 8**

**Greatest common factor of 6 and 15**

Factors of 6 = 1, 2, 3, and 6

Factors of 15 = 1, 3, 5, and 15

Common factors of 6 and 15 = 1, 3**GCF of 6 and 15 = 3**

**Greatest common factor of 12 and 18**

Factors of 12 = 1, 2, 3, 4, 6, and 12

Factors of 18 = 1, 2, 3, 6, 9 and 18

Common factors of 12 and 18 = 1, 2, 3, and 6**GCF of 12 and 18 = 6**

**Greatest common factor of 27 and 36**

Factors of 27 = 1, 3, 9, and 27

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36

Common factors of 27 and 36 = 1, 3**GCF of 27 and 36 = 3**

### TRY IT NOW!

- GCF of 30 and 75
- GCF of 25 and 70
- GCF of 48 and 84
- GCF of 75 and 100
- GCF of 24, 40, and 50

**Answer**

1 . 15

2 . 5

3 . 12

4 . 25

5 . 2