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How It Works
The Greatest Common Factor (GCF), also called GCD, is the largest integer that divides both numbers evenly. This calculator uses Euclid's algorithm: repeatedly divide the larger number by the smaller and take the remainder until the remainder is zero. The last non-zero remainder is the GCF.
Example Problem
Find GCF(24, 36):
- 36 = 1 × 24 + 12
- 24 = 2 × 12 + 0
GCF = 12
Frequently Asked Questions
What is the GCF of two numbers?
The GCF is the largest number that divides both values without a remainder. For 18 and 24, the GCF is 6 because 6 is the biggest number that goes into both evenly.
How is GCF used to simplify fractions?
Divide both the numerator and denominator by their GCF. For 8/12, the GCF of 8 and 12 is 4, so 8/12 simplifies to 2/3.
What is the difference between GCF and LCM?
GCF is the largest shared factor; LCM is the smallest shared multiple. They are related by the formula LCM(a, b) = |a × b| / GCF(a, b). For 12 and 18, GCF = 6 and LCM = 36.
Related Calculators
- LCM Calculator — find the Least Common Multiple of two numbers.
- Simplify Fraction Calculator — reduce fractions to lowest terms using GCF.
- Fraction Addition Calculator — add fractions with unlike denominators.
- Fraction Multiplication Calculator — multiply fractions and simplify using GCF.
- Fraction Division Calculator — divide fractions with step-by-step work.