GCF Calculator — Greatest Common Factor of Multiple Numbers
Enter two or more whole numbers to find their greatest common factor (GCF) — the largest number that divides all of them evenly. Also shows all common factors, the LCM, and a simplified fraction when two numbers are given.
Largest integer that divides every number in the list without a remainder
这个计算器是如何工作的？
GCF of a list is found by repeatedly applying GCF(a, b) = GCF(b, a mod b) (Euclidean algorithm) pairwise. GCF(24, 36, 48) = 12. All factors of the GCF are common to every number in the list. Use the GCF to reduce fractions to lowest terms: divide numerator and denominator by GCF.
公式
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 a remainder. For a list of numbers, it is computed by folding the Euclidean algorithm left: GCF(a, b, c) = GCF(GCF(a, b), c).
Every divisor of the GCF is automatically a divisor of all numbers in the list, so the "all common factors" list is simply the factor list of the GCF itself. This means GCF(24, 36, 48) = 12, and the shared factors are 1, 2, 3, 4, 6 and 12.
When exactly two numbers are entered, the calculator also shows the simplified fraction: divide numerator and denominator by the GCF to get the lowest terms. The LCM is derived from the identity LCM(a, b) = |a × b| ÷ GCF(a, b) for pairs, extended leftward for larger lists.
常见问题
Divide both the numerator and the denominator by their GCF. For example, 24/36 → GCF = 12 → 24/12 = 2 and 36/12 = 3, giving the simplified fraction 2/3.
Yes. Greatest common factor (GCF), greatest common divisor (GCD), and highest common factor (HCF) all refer to the same value — the largest integer that divides all numbers in the set exactly.
GCF(n, 1) = 1 for any positive integer n, because 1 is the only positive integer that divides 1, and it divides every integer.
也称为
TG we-Calculate Editorial Team. (2026). GCF Calculator — Greatest Common Factor of Multiple Numbers [Online calculator]. TG we-Calculate. https://we-calculate.com/zh/calculator/gcf-calculator
TG we-Calculate Editorial Team. "GCF Calculator — Greatest Common Factor of Multiple Numbers." TG we-Calculate. 2026. https://we-calculate.com/zh/calculator/gcf-calculator.
TG we-Calculate Editorial Team, "GCF Calculator — Greatest Common Factor of Multiple Numbers," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/zh/calculator/gcf-calculator
@misc{wecalculate_gcf_calculator, title = {GCF Calculator — Greatest Common Factor of Multiple Numbers}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/zh/calculator/gcf-calculator}}, year = {2026}, note = {TG we-Calculate} }
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