GCF Calculator
Find the Greatest Common Factor of up to 10 numbers. Uses prime factorization, the Euclidean algorithm, and factor listing — with step-by-step solutions and fraction simplification.
6
GCF
36
LCM
No
COPRIME?
Enter Numbers
Enter 2-10 positive integers to find their Greatest Common Factor
Quick Examples
Greatest Common Factor
6
GCF of 12, 18
6
GCF
36
LCM
216
GCF × LCM
No
Coprime?
All Factors — Common Ones Highlighted
Factors of 12:
Factors of 18:
Common Factors of All Numbers
Prime Factorization — Shared Factors Highlighted
GCF = Product of Shared Primes (Min Powers)
GCF = 2 × 3 = 6
Euclidean Algorithm
Repeatedly divide and take the remainder until the remainder is 0. The last non-zero remainder is the GCF.
- 112 = 0 × 18 + 12
- 218 = 1 × 12 + 6
- 312 = 2 × 6 + 0← Remainder = 0, GCF = 6
Step-by-Step (Prime Factorization Method)
- 1List the numbers12, 18
- 2Prime factorize each12 = 2² × 3 · 18 = 2 × 3²
- 3Find common primes (appear in ALL numbers)2, 3
- 4Take lowest power of each common prime2: min power across all numbers = 1 · 3: min power across all numbers = 1
- 5Multiply the common prime powers togetherGCF = 2 × 3 = 6
- 6Verify: all numbers divisible by GCF12 ÷ 6 = 2 · 18 ÷ 6 = 3
Simplify Fractions Using GCF
Using the first two numbers as numerator/denominator — divide both by GCF to simplify.
Original Fraction
12/18
÷6 Simplified Form
2/3
Decimal
0.666667
GCF(12, 18) = 6 → Divide both by 6 → 12/18 = 2/3
What Is the Greatest Common Factor (GCF)?
The Greatest Common Factor (GCF) — also called Greatest Common Divisor (GCD) or Highest Common Factor (HCF) — is the largest integer that divides all given numbers without a remainder. GCF is essential for simplifying fractions, factoring polynomials, and solving problems that split quantities into equal groups.
Three Methods to Find GCF
Method 1 — Prime Factorization: factor each number, then take only the SHARED primes at their LOWEST power. GCF(12,18): 12=2²×3, 18=2×3² → shared 2¹ and 3¹ → GCF = 2 × 3 = 6Method 2 — Euclidean Algorithm: repeatedly replace (a, b) with (b, a mod b) until b = 0 → GCF(48,18): 48=2×18+12 → 18=1×12+6 → 12=2×6+0 → GCF = 6Method 3 — Listing Factors: Factors of 12: 1,2,3,4,6,12. Factors of 18: 1,2,3,6,9,18 → largest common factor = 6The Euclidean algorithm is by far the fastest of the three for large numbers — it needs only a handful of division steps no matter how big the inputs get, while listing every factor gets slow quickly. Prime factorization is slower for large numbers but is the most instructive: it shows exactly which shared building blocks make up the GCF, which is why this calculator displays both methods side by side rather than picking just one.
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Simplify Fractions
Divide numerator and denominator by their GCF to reduce any fraction to lowest terms in one step.
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Split Into Equal Groups
The GCF gives the largest number of identical groups you can make from several quantities with nothing left over.
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Factor Expressions
In algebra, pulling out the GCF of a set of terms is usually the first step before factoring further.
— FAQ