Find the Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), of two or more integers. Also shows LCM and Euclidean algorithm steps.
| Number | Prime Factors |
|---|---|
| 48 | 2^4 × 3 |
| 36 | 2^2 × 3^2 |
| 24 | 2^3 × 3 |
| GCF = 12 | 2^2 × 3 |
| Term | Meaning |
|---|---|
| GCF / GCD | Largest integer that divides all given numbers evenly |
| LCM | Smallest positive integer divisible by all given numbers |
| Co-prime | GCF = 1 (no common factors except 1) |
Step-by-step for the first two numbers.
| Step | Division | Remainder |
|---|---|---|
| 1 | 48 = 1 × 36 + 12 | 12 |
| 2 | 36 = 3 × 12 + 0 | 0 |
| Step | Calculation | Result |
|---|---|---|
| 1 | GCF(48, 36) | 12 |
| 2 | GCF(12, 24) | 12 |
| Property | Formula |
|---|---|
| For two numbers | GCF(a,b) × LCM(a,b) = a × b |
| LCM from GCF | LCM = (a × b) / GCF(a,b) |
| Euclidean step | GCF(a,b) = GCF(b, a mod b) |