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The greatest common divisor (GCD) of a number of integers is the greatest number that all the integers can be divided by without getting a fractional part. For example, the greatest common divisor of 6 and 9 is 3 because 3 is the greatest number that divides both 6 and 9.
The greatest common divisor can be used to simplify fractions. To reduce a fraction as much as possible the numerator and denominator can be divided by the greatest common divisor for all terms in the numerator and denominator.
The fraction 6 ⁄ 9 can in this way be simplified by dividing the numerator and denominator by GCD(6, 9) = 3.
This works even for fractions that contain more complicated expressions. The fraction (2x + 8y) ⁄ 4 can be simplified by dividing by GCD(2, 8, 4) = 2.
Another possible use case is when doing factorizations of polynomial expressions. The expression 8x2 + 12x can be factorized using the factor 4 because GCD(8, 12) = 4.