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Greatest Common Factor
Find GCF of numbers
How It Works
The greatest common factor (GCF), also known as the greatest common divisor, of two (or more) non-zero integers a and b, is the largest positive integer by which both integers can be divided. It is commonly denoted as GCF(a, b).
In mathematics, the greatest common factor (GCF), also known as the greatest common divisor, of two (or more) non-zero integers a and b, is the largest positive integer by which both integers can be divided. It is commonly denoted as GCF(a, b).
Prime Factorization Method: Compute the prime factorizations of each integer, determine which factors they have in common, and multiply these factors to find the GCD. This method is only efficient for smaller integer values.
Euclidean Algorithm: A far more efficient method. The algorithm is based on the observation that the GCD of two integers can also divide their difference. In practice: (1) Given two positive integers a and b where a > b, subtract b from a to arrive at c. (2) Continue subtracting b from a until c < b. (3) Use b as the new large number and subtract c, repeating until the remainder is 0. (4) Once the remainder is 0, the GCF is the remainder from the step preceding the zero result.
Results
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Quick Tips
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