


Description 



Common Factor: A number (or an algebraic expression) that is a factor of two or more numbers (or algebraic expressions). 
Examples
Numbers 
Factors 
Common Factors 
GCF 
15 
±1, ±3, ±5, ±15 
±1, ±5 
5 
25 
±1, ±5, ±25 
Numbers 
Factors 
Common Factors 
GCF 
36 
±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18,
±36 
±1, ±2, ±3, ±4, ±6, ±12 
12 
24 
±1, ±2, ±3, ±4, ±6, ±8, ±12,
±24 
Numbers 
Factors 
Common Factors 
GCF 
30 
±1, ±2, ±3, ±5, ±6, ±10, ±15, ±30 
±1, ±2, ±5, ±10 
10 
20 
±1, ±2, ±4, ±5, ±10,
±20 
Example of Relatively Prime
Numbers
Numbers 
Factors 
Common Factor 
GCF 
32 
±1, ±2, ±4, ±8, 16, ±32 
±1 
1 
65 
±1, ±5, ±13,
±65 
Note that neither 32 nor 65 is
prime. Since they have the number 1 as their only common factor, 32 and 65 are
relatively prime to each other.
Common Factors in Algebraic Terms
Consider the terms 6x^{2} and 15xy. The common factors are 3, x, and 3x. Now consider the terms 3xy and 5(x + y). The common factor is only 1, because those are unlike terms and their coefficients are relatively prime. If those were like 3xy and 6(x + y), then the common term would be 3 since it divides the coefficients.


