Enter values and select Calculate.
Calculated result
How to use this calculator
- Enter two to 50 integers separated by commas, spaces, or line breaks.
- Negative signs are accepted and absolute values determine common factors.
- Calculate to see the exact GCF and bounded Euclidean steps.
- Use the related LCM calculator for the smallest common multiple instead.
Formula and method
The Euclidean algorithm repeatedly replaces (a, b) with (b, a mod b) until the remainder is zero. For a list, reduce the result pairwise.
Worked example
For 24, 36, and 60, gcd(24,36) is 12 and gcd(12,60) remains 12, so the GCF is 12.
Assumptions and limits
- Integer components may contain up to 100 digits.
- gcd(0,n) equals the absolute value of n.
- Duplicate values are valid.
- The displayed explanation is capped to avoid excessive output.
Understanding the result
The result follows the displayed deterministic method. Exact-integer operations use BigInt where appropriate, and any controlled precision limit is stated before the related output can be interpreted.
Common mistakes
- Entering decimals or fractions
- Confusing greatest common factor with least common multiple
- Assuming negative signs make the GCF negative
- Using prime-factor guessing for very large values
Methodology note
The calculator uses the arithmetic definitions shown on this page. It does not call an external calculator service, evaluate expressions, or infer unselected mathematical conventions.
This deterministic utility is a calculation aid. Confirm required notation, precision, and course or professional conventions separately.