GCF / GCD Calculator
Find the Greatest Common Factor (GCF, also called GCD) of 2 to 5 numbers. See the complete Euclidean algorithm step by step and the LCM.
Enter 2 to 5 positive integers.
Euclidean Algorithm
The Euclidean algorithm finds GCF by repeatedly applying: GCF(a, b) = GCF(b, a mod b), until the remainder is 0.
Frequently Asked Questions
The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), is the largest positive integer that divides all given numbers without a remainder.
An efficient algorithm to compute GCF: divide the larger number by the smaller and take the remainder. Repeat with the smaller number and the remainder until the remainder is zero. The last non-zero remainder is the GCF.
If GCF(a, b) = 1, the numbers are called coprime or relatively prime. They share no common prime factors. For example, GCF(8, 9) = 1.
To simplify a fraction a/b, divide both numerator and denominator by GCF(a, b). For example, 12/18 → GCF = 6 → 2/3.
No. The GCF is always less than or equal to the smallest of the given numbers, since a common factor must divide all numbers, and no number can have a divisor larger than itself (except in trivial cases).
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