GCF Calculator

The Greatest Common Factor (GCF) — also called the Greatest Common Divisor (GCD) — is the largest number that divides evenly into two or more numbers. It's essential for simplifying fractions and solving division problems.

How to Use This Calculator

1. Enter two or more positive integers (separated by commas).
2. Click Calculate to find the GCF with prime factorization steps shown.

Methods to Find GCF

Prime Factorization: Factor each number, identify common prime factors at their lowest power.
18 = 2 × 3² | 24 = 2³ × 3 → Common: 2¹ × 3¹ = GCF = 6

Euclidean Algorithm: GCF(a, b) = GCF(b, a mod b). Repeat until remainder = 0.
GCF(48, 18): 48 mod 18 = 12 → 18 mod 12 = 6 → 12 mod 6 = 0 → GCF = 6

List factors: List all factors, pick the largest shared one. (Works best for small numbers.)

Example Calculations

• GCF(12, 18) = 6
• GCF(100, 75) = 25
• GCF(7, 13) = 1 (coprime — share no common factors)
• GCF(24, 36, 48) = 12

Real-World Uses

• Simplifying fractions: 18/24 ÷ GCF(6) = 3/4
• Distributing evenly: Splitting 18 apples and 24 oranges into identical groups → 6 groups of 3 apples and 4 oranges
• Tile problems: Largest square tile fitting a 18×24 room without cutting = 6-inch tiles

Common Mistakes to Avoid

• Confusing GCF with LCM — GCF is the largest common factor (≤ both numbers). LCM is the smallest common multiple (≥ both numbers).
• Forgetting GCF of two identical numbers = the number itself — GCF(7, 7) = 7.
• GCF = 1 means coprime, not that there is no GCF — All pairs of integers have a GCF; when it's 1, the numbers are coprime.

Frequently Asked Questions

When is GCF useful in fractions?

Dividing numerator and denominator by their GCF reduces a fraction to lowest terms. 36/48: GCF = 12 → 36÷12 / 48÷12 = 3/4. See our Fraction Calculator.

Can GCF be found for more than two numbers?

Yes. Find GCF of the first two, then find GCF of that result with the next number. GCF(12, 18, 24): GCF(12,18)=6, then GCF(6,24)=6.

Is GCF the same as GCD?

Yes — GCF (Greatest Common Factor) and GCD (Greatest Common Divisor) are the same concept with different names. GCF is more commonly used in the US; GCD is more common in higher mathematics.

Conclusion

GCF is a cornerstone concept in number theory with everyday applications in fraction simplification and distribution problems. Use this calculator to find GCF instantly for any set of integers.

Related: LCM Calculator | Fraction Calculator | Factor Calculator