Find the greatest common factor of two or more numbers using prime factorisation, with step-by-step working and factor lists.
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Number Theory
A GCF calculator finds the greatest common factor (also called greatest common divisor) of two or more integers. The GCF is the largest number that divides each input evenly and is essential for simplifying fractions, factoring expressions, and solving divisibility problems.
The greatest common factor of a set of numbers is the largest positive integer that divides every number in the set without leaving a remainder. It captures the shared structure of the numbers and is widely used in fraction simplification, ratio reduction, and algebraic factoring.
For two numbers, the GCF can be found by listing factors, using prime factorisation, or applying the Euclidean algorithm. Each method produces the same result.
The Euclidean algorithm is an efficient method for computing the GCF. It repeatedly replaces the larger number with the remainder of dividing the larger by the smaller until the remainder is zero. The last non-zero remainder is the GCF.
GCF(a, b) = GCF(b, a mod b), until remainder = 0
Replace a with b and b with the remainder of a divided by b. Repeat until the remainder is zero; the last non-zero value is the GCF.
Dividing both the numerator and denominator of a fraction by their GCF reduces the fraction to lowest terms in a single step. This is why GCF calculation is a core skill in fraction arithmetic.
Frequently asked questions
Yes. Greatest common factor and greatest common divisor are two names for the same concept. GCF is more common in American maths education, while GCD is used more widely in number theory and computing.
If two numbers are both prime and different, their only shared factor is one, so their GCF is one. Numbers with a GCF of one are called coprime or relatively prime.
Yes. Compute the GCF of the first two numbers, then find the GCF of that result with the third number, and so on. The process works for any number of inputs.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Find the least common multiple or greatest common divisor of two whole numbers with step-by-step working.
Find all factors of any positive integer, displayed as individual factors and factor pairs, with a prime-or-composite check.
Break any positive integer into its prime factors, displayed as a factor tree and in exponential notation.
Reduce any fraction to its simplest form by dividing the numerator and denominator by their greatest common factor.
