GCF Calculator (Greatest Common Factor)

The GCF is the largest positive integer that divides every number in a set without leaving a remainder. It is also called the greatest common divisor (GCD). For 12 and 18, that number is 6, because 6 divides both and no larger integer does.

For small numbers, list all factors of each number and pick the largest one they share. For larger numbers, use the Euclidean algorithm: replace the bigger number with the remainder of dividing the two, and repeat until the remainder is 0. The last non-zero remainder is the GCF. For example, gcd(48, 18) gives gcd(18, 12), then gcd(12, 6), then gcd(6, 0) = 6.

The GCF of 12 and 18 is 6. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The largest factor both lists share is 6.

Yes. The calculator reduces the list pair by pair: it computes gcd(first, second), then gcd(that result, third), and so on. Enter as many integers as you need, separated by commas or spaces, and you get the GCF of the entire set.

No. The GCF is the largest integer that divides all inputs, while the LCM (least common multiple) is the smallest integer that all inputs divide evenly into. For any two positive integers a and b, GCF x LCM = a x b. For 12 and 18: GCF = 6, LCM = 36, and 6 x 36 = 12 x 18 = 216.

Their GCF is 1, and the numbers are called coprime, or relatively prime. For example, 8 and 15 share no factors other than 1, so gcd(8, 15) = 1. This comes up often in fractions: a fraction is already in lowest terms when its numerator and denominator are coprime.

Yes. GCF is conventionally defined as a positive integer, so the calculator takes the absolute value of each input before computing. Entering -12 and 18 gives the same result as 12 and 18: a GCF of 6.