What is the difference between GCF and LCM?

The GCF is the largest number that divides all given numbers. The LCM is the smallest number that all given numbers divide into. They are related by: GCF(a,b) × LCM(a,b) = a × b.

How is the GCF used to simplify fractions?

Divide both the numerator and denominator by their GCF. For example, 24/36 simplifies to 2/3 because GCF(24, 36) = 12.

What is the GCF of two prime numbers?

The GCF of two different prime numbers is always 1, since primes have no common factors other than 1.

What does it mean if the GCF is 1?

If GCF(a, b) = 1, the numbers are called coprime or relatively prime. They share no common factors other than 1.

Can I find the GCF of more than two numbers?

Yes. Apply the Euclidean algorithm pairwise: GCF of three numbers equals GCF(GCF(a, b), c). This calculator handles any number of inputs.

Math

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GCF Calculator

Find the Greatest Common Factor (GCF / GCD) of two or more numbers using the Euclidean algorithm.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.

📌 Direct Answer & Summary

The Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD), is the largest integer that divides two or more numbers without leaving a remainder. It is essential for simplifying fractions, reducing ratios, and solving number theory problems.

Enter numbers (comma or space separated, 2 or more)

What is GCF Calculator?

How to use it

1️⃣ Enter two or more integers separated by commas or spaces.
2️⃣ The GCF appears instantly along with the full factor list for each number.
3️⃣ The 'Common factors' panel shows all shared factors, not just the greatest one.
4️⃣ You can enter as many numbers as you like — the calculator finds the GCF of the entire set.

Formula

The Euclidean algorithm: GCF(a, b) = GCF(b, a mod b), repeated until the remainder is 0. For multiple numbers: GCF(a, b, c) = GCF(GCF(a, b), c).

💡 See it in action — a real example

To find GCF(48, 36): 48 mod 36 = 12, then 36 mod 12 = 0, so GCF = 12. For GCF(48, 36, 84): GCF(48, 36) = 12, then GCF(12, 84) = 12.

❓ Common questions

What is the difference between GCF and LCM?: The GCF is the largest number that divides all given numbers. The LCM is the smallest number that all given numbers divide into. They are related by: GCF(a,b) × LCM(a,b) = a × b.
How is the GCF used to simplify fractions?: Divide both the numerator and denominator by their GCF. For example, 24/36 simplifies to 2/3 because GCF(24, 36) = 12.
What is the GCF of two prime numbers?: The GCF of two different prime numbers is always 1, since primes have no common factors other than 1.
What does it mean if the GCF is 1?: If GCF(a, b) = 1, the numbers are called coprime or relatively prime. They share no common factors other than 1.
Can I find the GCF of more than two numbers?: Yes. Apply the Euclidean algorithm pairwise: GCF of three numbers equals GCF(GCF(a, b), c). This calculator handles any number of inputs.

⚡ Related Math Tools & Calculators

LCM Calculator Prime Number Calculator Fraction Calculator