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- Enter two or more whole numbers separated by commas or spaces.
- The GCF appears instantly. For two numbers, the Euclidean algorithm steps are listed.
Formel
The Euclidean algorithm repeatedly replaces the larger number with the remainder of dividing it by the smaller one. When the remainder is 0, the last non-zero remainder is the GCF. For more than two numbers, GCF(a, b, c) = GCF(GCF(a, b), c).
gcd(a, b) = gcd(b, a mod b)
gcd(a, 0) = a
Example
- GCF(180, 48): 180 = 3 × 48 + 36.
- 48 = 1 × 36 + 12; 36 = 3 × 12 + 0.
- GCF = 12. With 300 as well: GCF(12, 300) = 12.
Häufige Fragen
What is the GCF used for?
Simplifying fractions (divide top and bottom by the GCF), factoring algebraic expressions and splitting items into equal groups.
What if the GCF is 1?
The numbers are coprime (relatively prime): they share no common factor other than 1.
How are GCF and LCM related?
For two positive integers, GCF(a, b) × LCM(a, b) = a × b.