GCF Calculator

Find the Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), of two or more integers. Also shows LCM and Euclidean algorithm steps.

Input

GCF / GCD
12
of 48, 36, 24
LCM
144

Prime Factorizations

NumberPrime Factors
482^4 × 3
362^2 × 3^2
242^3 × 3
GCF = 122^2 × 3
TermMeaning
GCF / GCDLargest integer that divides all given numbers evenly
LCMSmallest positive integer divisible by all given numbers
Co-primeGCF = 1 (no common factors except 1)

Euclidean Algorithm Steps

Step-by-step for the first two numbers.

StepDivisionRemainder
148 = 1 × 36 + 1212
236 = 3 × 12 + 00
GCF(48, 36) = 12

Multi-number GCF Chain

StepCalculationResult
1GCF(48, 36)12
2GCF(12, 24)12

GCF × LCM Relationship

PropertyFormula
For two numbersGCF(a,b) × LCM(a,b) = a × b
LCM from GCFLCM = (a × b) / GCF(a,b)
Euclidean stepGCF(a,b) = GCF(b, a mod b)