Greatest Common Factor
Finding the Greatest Common Factor Here are three ways:
1. You can:
Two Numbers All Factors Common Factors Greatest
Common Factor Example Simplified
Fraction 9 and 12 9: 1,3,9
12: 1,2,3,4,6,12 1,3 3 9/12 » 3/4 And another example:
Two Numbers All Factors Common Factors Greatest
Common Factor Example Simplified
Fraction 6 and 18 6: 1,2,3,6
18: 1,2,3,6,9,18 1,2,3,6 6 6/18 » 1/3 2. You can find the prime factors and combine the common ones together:
Two Numbers Thinking ... Greatest
Common Factor Example Simplified
Fraction 24 and 108 2 × 2 × 2 × 3 = 24, and
2 × 2 × 3 × 3 × 3 = 108 2 × 2 × 3 = 12 24/108 » 2/9 3. And sometimes you can just play around with the factors until you discover it:
Two Numbers Thinking ... Greatest
Common Factor Example Simplified
Fraction 9 and 12 3 × 3 = 9 and 3 × 4 = 12 3 9/12 » 3/4 But in that case you had better be careful you have found the greatest common factor.
1. You can:
- find all factors of both numbers (I have an All Factors Tool to help you),
- then select the ones that are common to both, and
- then choose the greatest.
Two Numbers All Factors Common Factors Greatest
Common Factor Example Simplified
Fraction 9 and 12 9: 1,3,9
12: 1,2,3,4,6,12 1,3 3 9/12 » 3/4 And another example:
Two Numbers All Factors Common Factors Greatest
Common Factor Example Simplified
Fraction 6 and 18 6: 1,2,3,6
18: 1,2,3,6,9,18 1,2,3,6 6 6/18 » 1/3 2. You can find the prime factors and combine the common ones together:
Two Numbers Thinking ... Greatest
Common Factor Example Simplified
Fraction 24 and 108 2 × 2 × 2 × 3 = 24, and
2 × 2 × 3 × 3 × 3 = 108 2 × 2 × 3 = 12 24/108 » 2/9 3. And sometimes you can just play around with the factors until you discover it:
Two Numbers Thinking ... Greatest
Common Factor Example Simplified
Fraction 9 and 12 3 × 3 = 9 and 3 × 4 = 12 3 9/12 » 3/4 But in that case you had better be careful you have found the greatest common factor.
