GCF
Calculator

Calculate the Greatest Common Factor of two or more numbers with Euclidean algorithm steps and prime factorization.

Input Numbers

Euclidean Algorithm

48 = 18 × 2 + 12
18 = 12 × 1 + 6
12 = 6 × 2 + 0

Prime Factorization

48 = 2^4 x 3
18 = 2 x 3^2

Result

GCF (Greatest Common Factor)

6

LCM (Least Common Multiple)

144

Numbers: 48, 18

Learn more

How does the Euclidean algorithm find the GCF efficiently?

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Frequently Asked Questions

The GCF of two or more integers is the largest positive integer that divides all of them without a remainder. For 12 and 18, the GCF is 6 because 6 is the largest number that divides both evenly.

Divide the larger number by the smaller and take the remainder. Replace the larger number with the smaller and the smaller with the remainder, then repeat until the remainder is zero. The last non-zero remainder is the GCF.

Dividing both the numerator and denominator of a fraction by their GCF reduces the fraction to its simplest form. For 12/18, dividing both by the GCF of 6 gives the simplified fraction 2/3.

GCF Calculator - Greatest Common Factor | ToolsCanvas