What is the Greatest Common Factor:
The greatest common factor or GCF is the largest positive integer that divides evenly into all numbers with zero remainder
How to find the Greatest Common Factor:
To find the greatest common factor between two numbers: first list all the factors for each number.
For example to find the GCF between 18 and 27 first list the factors of 18 and 27 separately:
18: 1, 2, 3, 6, 9, 18
27: 1, 3, 9, 27
18: 1, 2, 3, 6, 9, 18
27: 1, 3, 9, 27
The common factors between 18 and 27 are 1, 3, 9.
The greatest common factor of 18 and 27 then is 9.
Sample Math Problems
1: Find the greatest common factor of 20, 50, and 120.
Answer:
First list the factors of 20, 50 and 120 separately
20: 1, 2, 4, 5, 10, 20
50: 1, 2, 5, 10, 25, 50
120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The common factors of 20, 50 and 120 are 1, 2, 5, 10
The greatest common factor then is 10.
2: What is the greatest common factor between 15 and 100?
Answer:
First list the factors of 20, 50 and 120 separately
15: 1, 3, 5, 15
100: 1, 2, 4, 5, 20, 25, 50, 100
The common factors of 15 and 100 is 1 and 5
The greatest common factor then is 5
3. What is the greatest common factor between 8, 18, and 48 ?
Answer:
8: 1, 2, 4, 8
8: 1, 2, 4, 8
18: 1, 2, 3, 6, 9, 18
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The common factors are: 1 and 2
The greatest common factor then is 2
4. What is the greatest common factor between 18 and 21?
Answer:
18: 1, 2, 3, 6, 9, 18
21: 1, 3, 7, 21
The common factors are 1, and 3
The greatest common factor then is 3
