Greatest Common Factor Calculator — GCF of Multiple Numbers
Enter two or more positive whole numbers to find their Greatest Common Factor (GCF) — the largest integer that divides all of them exactly — plus a complete list of all shared factors and step-by-step Euclidean algorithm working.
Largest positive integer that divides all entered numbers without remainder
48 ÷ 36
36 ÷ 12
Remainder is 0 — the last non-zero remainder is the GCF
How does this calculator work?
Enter 2+ positive whole numbers to find their GCF — the largest integer dividing all of them. GCF is computed via the Euclidean algorithm (repeated remainders), folded across the list. All common factors are the factors of the GCF. Enter the numbers to see GCF, all shared factors, and step-by-step working.
Formula
How this is calculated
The Greatest Common Factor (GCF) — also called the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) — is the largest positive integer that divides every number in a set without leaving a remainder. For example, the GCF of 48, 36 and 60 is 12, because 12 is the largest number that goes into all three evenly.
The calculator finds the GCF by applying the Euclidean algorithm: for any two positive integers a and b, repeatedly replace the larger with the remainder of a ÷ b until the remainder is zero; the last non-zero value is the GCF. For more than two numbers, this operation is folded left — GCF(a, b, c) = GCF(GCF(a, b), c) — which works because the GCF of a set is the same no matter how you group the numbers.
Once the GCF is known, all common factors of the entire set are simply the factors of the GCF itself. A number is a common factor if and only if it divides the GCF. This list is shown in the results alongside the step-by-step algorithm trace for the first pair of numbers. The GCF is used to simplify fractions, solve ratio problems, and find how to split sets into equal groups.
Frequently asked questions
They are the same value with different names. GCF (Greatest Common Factor) and HCF (Highest Common Factor) are common in K-12 math; GCD (Greatest Common Divisor) is the standard mathematical term. All describe the largest integer that divides every number in the set without remainder.
Divide both the numerator and denominator by their GCF. For example, to simplify 36/48: GCF(36, 48) = 12, so 36 ÷ 12 = 3 and 48 ÷ 12 = 4, giving 3/4. The result is the fraction in its lowest terms.
Any number that divides all integers in the set must also divide their GCF (because GCF is a linear combination of the inputs). Conversely, any factor of the GCF divides the GCF, which in turn divides each input. So common factors and factors of the GCF are exactly the same set.
Also known as
TG we-Calculate Editorial Team. (2026). Greatest Common Factor Calculator — GCF of Multiple Numbers [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/greatest-common-factor-calculator
TG we-Calculate Editorial Team. "Greatest Common Factor Calculator — GCF of Multiple Numbers." TG we-Calculate. 2026. https://we-calculate.com/calculator/greatest-common-factor-calculator.
TG we-Calculate Editorial Team, "Greatest Common Factor Calculator — GCF of Multiple Numbers," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/greatest-common-factor-calculator
@misc{wecalculate_greatest_common_factor_calculator, title = {Greatest Common Factor Calculator — GCF of Multiple Numbers}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/greatest-common-factor-calculator}}, year = {2026}, note = {TG we-Calculate} }
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