math ToolUpdated 2026-09-19
GCF Calculator (Greatest Common Factor)
Find the greatest common factor (GCF) between integers using the Euclidean algorithm.
Formula & Mathematical Methodology
gcd(a, b) = gcd(b, a mod b)
The Euclidean algorithm repeatedly replaces the larger number with the remainder until the remainder is 0.
How to Use This GCF Calculator (Greatest Common Factor)
- Enter two integers.
- Click Calculate to determine their largest shared divisor.
Step-by-Step Worked Example
Scenario: GCF of 48 and 72
1. 72 mod 48 = 24
2. 48 mod 24 = 0
3. The GCF is 24
Final Calculated Result: 24
What Does Your Result Mean?
The highest common number that divides both inputs without any remainder.
Common Practical Applications:
- Fraction simplification
- Tile cutting and carpentry divisions
- Algebraic factoring
Important Limitations & Assumptions:
- Inputs must be non-zero integers.
Frequently Asked Questions
What is the difference between GCF and LCM?
GCF is the largest factor dividing both numbers; LCM is the smallest multiple shared by both.
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