﻿ Definition and examples greatest common factor | define greatest common factor - Algebra - Free Math Dictionary Online

# 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

### Solved Examples on Greatest Common Factor

• A. 20
• B. 4
• C. 36
• D. 180

#### 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

• A. 5
• B. 10
• C. 15
• D. 20

#### 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

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