Find the exact nonnegative greatest common factor of signed integers, inspect Euclidean steps and calculate the LCM when all inputs are nonzero.
01 / INPUTS & ASSUMPTIONS
02 / RESULT & EXPLANATION
| Magnitude | Prime factorization | Positive factors |
|---|---|---|
| 48 | 2^4 × 3 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 |
| 180 | 2^2 × 3^2 × 5 | 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 |
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Use exact Euclidean remainders for large signed integers while keeping factorization and factor-list work within small documented bounds.
GCF Calculator inputs and calculations remain in browser memory. No external processing service receives entered values. Existing website infrastructure may log ordinary page requests; copying occurs only when selected.
The greatest common factor is the largest nonnegative integer dividing every entered integer. GCD, greatest common divisor, is another name for the same value.
GCF calculations use absolute magnitudes, so GCF(-18, 24) = 6. The result is nonnegative and is not affected by the signs of the inputs.
GCF(0, n) equals the absolute value of nonzero n. An all-zero list, including GCF(0, 0), is explicitly treated as undefined and rejected.
The exact BigInt Euclidean algorithm repeatedly replaces a pair by divisor and remainder until the remainder is zero. At most 60 steps are displayed, while the full bounded-input calculation completes exactly.
An exact multi-integer LCM is shown when every entered magnitude is nonzero. Each step divides by the GCF before multiplying to reduce intermediate size. Lists containing zero omit the LCM in this tool.
Prime factorization is limited to magnitudes at most 1,000,000 and factor lists to 10,000. Large integers still receive an exact GCF and eligible LCM without brute-force factoring. Use two to ten signed integers with at most 60 digits each.