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GCF Calculator
Find the greatest common factor of 2+ numbers with steps.
Quick answer
How do you find the GCF of two numbers?
Break each number into primes and multiply the primes they share. 48 = 2⁴ × 3 and 18 = 2 × 3², so the GCF is 2 × 3 = 6. Or divide and keep remainders: 48 = 2 × 18 + 12, 18 = 1 × 12 + 6, 12 = 2 × 6 + 0 → GCF = 6.
GCF = product of the prime factors every number shares, each at its lowest power. Euclid: GCF(a, b) = GCF(b, a mod b), repeated until the remainder is 0.
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- Method 1 — prime factorization:
- 48 = 2^4 × 3
- 18 = 2 × 3^2
- Multiply the shared primes at their lowest power: GCF = 2 × 3 = 6
- Method 2 — Euclidean algorithm (divide, keep the remainder, repeat until 0):
- 48 = 2 × 18 + 12
- 18 = 1 × 12 + 6
- 12 = 2 × 6 + 0
- The last non-zero remainder is the GCF: 6.
- Simplify 48/18: divide both by 6 → 8/3.
Find the greatest common factor (GCD/HCF) of 2 or more numbers with prime factorization and Euclidean algorithm steps.
About this GCF Calculator
The GCF Calculator finds the greatest common factor — also called the greatest common divisor (GCD) or highest common factor (HCF) — of two or more whole numbers. It shows two methods side by side: prime factorization and the Euclidean algorithm, so you can check homework either way.
What you'll need
- • Two or more whole numbers separated by commas
How it works
- 1. Type your numbers separated by commas.
- 2. The calculator breaks each into prime factors.
- 3. It multiplies the shared primes at their lowest power.
- 4. It double-checks with the Euclidean algorithm.
- 5. Read the GCF and every step.
Worked example
GCF of 12, 18, and 30: 12 = 2² × 3, 18 = 2 × 3², 30 = 2 × 3 × 5. Shared primes are 2 and 3, so GCF = 6.
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GCF Calculator FAQ
What is the GCF Calculator?
The GCF Calculator is a free online tool that helps you find the greatest common factor of 2+ numbers with steps.
How do I use the GCF Calculator?
Open the GCF Calculator, enter the requested values, and review the instant estimate on the page.
Is the GCF Calculator free?
Yes. The GCF Calculator is free to use on Fast Online Calculator and does not require an account.
What is the GCF of 24 and 36?
12. 24 = 2³ × 3 and 36 = 2² × 3², so the shared part is 2² × 3 = 12.
Is GCF the same as GCD and HCF?
Yes. Greatest common factor, greatest common divisor, and highest common factor are three names for the same number.
What if the GCF is 1?
The numbers are called relatively prime (or coprime) — they share no factor except 1, like 8 and 15.
How is the GCF used to simplify fractions?
Divide the top and bottom by the GCF. For 18/48 the GCF is 6, so 18/48 = 3/8.
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