Find the greatest common factor of two or more whole numbers—with common factors, prime factorizations, and every Euclidean step.
Use whole numbers. Negative values are accepted and calculated by absolute value.
12 divides every entered number with no remainder, and no larger positive integer does.
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 selected number without a remainder.
Choose the view that helps you learn or verify the answer.
Repeated division reduces large numbers quickly until the remainder is zero.
Prime factors show which building blocks all the numbers share.
The visual map highlights every common factor and the greatest one.
For small numbers, list every factor and choose the largest one present in all lists. For large numbers, use the Euclidean algorithm: divide the larger number by the smaller, replace the pair with the smaller number and the remainder, and repeat. With more than two numbers, calculate the GCF of the first pair, then combine that result with each remaining number.
Yes. Greatest common factor, greatest common divisor, and highest common factor are different names for the same value.
Yes. Numbers whose only shared positive factor is 1 are called relatively prime or coprime.
The sign does not change divisibility, so the calculator uses absolute values and returns a nonnegative GCF.
The GCF of zero and a nonzero number is the absolute value of the nonzero number. For all-zero inputs, this calculator displays 0 by convention.
