Common Factor Calculator Find all common factors, GCF, and common multiples — with prime visuals, real-world uses, and st...
Common Factor Calculator
Find all common factors, GCF, and common multiples — with prime visuals, real-world uses, and step-by-step math.
All Common Factors**:
→ Compute $G = \gcd(a, b, c, \dots)$ → List all divisors of $G$
GCF (Euclidean)**:
$$ \gcd(a, b) = \gcd(b, a \bmod b) \text{ until } b = 0 $$
GCF (Prime)**:
48 = 2⁴ × 3¹ 180 = 2² × 3² × 5¹ → GCF = 2min(4,2) × 3min(1,2) = 2² × 3 = **12**
✅ Pro Tip**: Every common factor divides the GCF — so just factor the GCF to get them all!
⚠️ Avoid these errors:
- Confusing factors & multiples** — Factors divide *into* the number (e.g., 1,2,3,4,6,12 for 12); multiples are *products* (12,24,36…)
- Ignoring 1** — 1 is *always* a common factor (and GCF = 1 means coprime)
- List all vs. prime only** — “Factors of 12” = {1,2,3,4,6,12}, *not* {2,3}
- Negative inputs** — GCF(−24,36) = GCF(24,36) = 12 (always positive)
✅ Real-World Uses**:
- Fractions**: Simplify 48/180 → divide by GCF=12 → **4/15**
- Tiling**: 120″ × 84″ room → largest square tile = **12″** (GCF)
- Ratios**: 24:36 → divide by 12 → **2:3**
| Numbers | Common Factors | GCF | LCM |
|---|---|---|---|
| 15, 25 | 1, 5 | 5 | 75 |
| 17, 23 | 1 | 1 | 391 |
| 24, 36 | 1, 2, 3, 4, 6, 12 | 12 | 72 |
| 97, 101 | 1 | 1 | 9,797 |
📉 Efficiency Tip**:
- To list factors of *n*: loop *i = 1 to √n* → if *i | n*, add *i* and *n/i*
- GCF(1,000,000, 1,000,001) = 1 (consecutive = coprime)
➡️ All Common Factors
“Common factors of 24 and 36?” → **1, 2, 3, 4, 6, 12**
➡️ GCF
“GCF of 48, 180, 60?” → **12**
➡️ Common Multiples
“First 5 common multiples of 6 and 8?” → **24, 48, 72, 96, 120**
Note: Handles up to 6 numbers. All inputs > 0. Output always positive integers. Zero inputs excluded (GCF(0,n)=n, but not standard for factor listing).