Math Tool✨ New Release
GCF Calculator
Find the Greatest Common Factor (GCF / GCD) of two or three numbers using the Euclidean algorithm, prime factorization, or list of common divisors.
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Interactive GCF Calculator Workspace
Greatest Common FactorGCF = 12
Euclidean Remainder Division
Start with Euclidean algorithm for 48 and 180:
48 = (180 × 0) + 48 (Remainder: 48)
180 = (48 × 3) + 36 (Remainder: 36)
48 = (36 × 1) + 12 (Remainder: 12)
36 = (12 × 3) + 0 (Remainder: 0)
The last non-zero remainder is 12.
Mathematical Formula & Variables
Equation Model
GCF(a, b) = GCF(b, a mod b) | GCF(a, b, c) = GCF(GCF(a, b), c)The Euclidean algorithm calculates GCF by repeatedly taking the remainder of the larger number divided by the smaller number until the remainder is zero.
Variable Definitions
| Symbol | Description |
|---|---|
| a, b, c | The positive integers for which you are calculating the GCF |
| mod | The modulo operation finding the integer remainder of division |
How to Use the GCF Calculator
- Enter two or three positive integers in the input fields.
- Click calculate to instantly see the GCF.
- Review the step-by-step Euclidean division path or prime factors comparisons.
Practical Example Calculation
Scenario Context: Finding the GCF of 48 and 180.
Step 1: Divide 180 by 48: 180 = (48 × 3) + 36. Remainder = 36.
Step 2: Divide 48 by remainder 36: 48 = (36 × 1) + 12. Remainder = 12.
Step 3: Divide 36 by remainder 12: 36 = (12 × 3) + 0. Remainder = 0.
Step 4: The last non-zero remainder is 12, which is the GCF.
The GCF of 48 and 180 is 12.
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