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 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 6x2 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.