## Greatest Common Factor

Finding the Greatest Common Factor Here are three ways:

Two Numbers All Factors Common Factors Greatest

Common Factor

Two Numbers All Factors Common Factors Greatest

Common Factor

Two Numbers Thinking ... Greatest

Common Factor

Two Numbers Thinking ... 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*

Fraction9 and 12Fraction

**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*

Fraction6 and 18Fraction

**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*

Fraction24 and 108Fraction

**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*

Fraction9 and 12Fraction

**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.