Greatest Common Factor (GCF)
Definition

In general, the greatest common factor (gcf) is the largest factor that a set of terms have in common.


Example 1: 6x3 is the greatest common factor of 12x7 and 18x3.


Example 2: 6x3y2 is the greatest common factor of 12x5y2z, 6x4y3z and 18x3y4.


Example 3: 2xy is a common factor of 12x5y2z, 6x4y3z and 18x3y4, but it is NOT the GREATEST common factor.


Example 4: 6x5 is NOT a COMMON factor of 12x5y2z, 6x4y3z and 18x3y4. It is therefore not the GREATEST common factor.


Example 5: 6x10 is NOT a factor of 12x5y2z, 6x4y3z or 18x3y4. It is therefore not the greatest common factor.


Definition (Natural Numbers)

In terms of numbers, the greatest common factor (gcf) is the largest natural number that exactly divides two or more given natural numbers.


Example 1: 6 is the greatest common factor of 12 and 18.


Example 2: 2 is a common factor of 12 and 18, but it is NOT the GREATEST common factor.


Example 3: 4 is NOT a COMMON factor of 12 and 18. It is therefore not the GREATEST common factor.


Example 4: 8 is NOT a factor of 12 or 18. It is therefore not the greatest common factor.


Demonstration Applet (Natural numbers)
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