## Related Words

# GREATEST COMMON FACTOR

## Definition of Greatest Common Factor

Greatest common factor is the greatest number that is a factor of each of two or more given numbers.

### More About Greatest Common Factor

Greatest Common Factor is abbreviated as G.C.F

Greatest common factor of two or more numbers can be found by successive division method and factorization method

### Examples of Greatest Common Factor:

The greatest common factor of 24 and 15 is 3

The greatest common factor of 40, 50, and 25 is 5

### Video Examples: Greatest Common Factor - GCF

### Solved Examples on Greatest Common Factor

**Ques: **Which is the greatest common factor of 20 and 36?

##### Choices:

- A. 20
- B. 4
- C. 36
- D. 180

Correct Answer: B

#### Solution:

- Step 1: The factors of 20 are 1, 2, 4, 5, 10, 20
- Step 2: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
- Step 3: The common factors of 20 and 36 are: 1, 2, 4
- Step 4: So, the greatest common factor or G.C.F. of 20 and 36 is 4

**Ques: **What is the G.C.F. of 45 and 75?

##### Choices:

- A. 5
- B. 10
- C. 15
- D. 20

Correct Answer: C

#### Solution:

- Step 1: Divide the larger number 75 by 45. The remainder will be 30

- Step 2: Divide 45 with the remainder 30. This time, the remainder is 15.

- Step 3: Finally, divide 30 with the remainder 15. The remainder is 0.

- Step 4: Therefore, the G.C.F. of 45 and 75 is 15