What is a common factor?

A common factor is a positive whole number that divides into two or more numbers completely without leaving any remainder.

What does it mean if two numbers have only 1 as a common factor?

If the only common factor between two numbers is 1 (GCF = 1), the numbers are termed 'relatively prime' or 'coprime' (such as 8 and 9).

What is the difference between GCF and LCM?

GCF is the largest number that divides evenly into all given numbers. LCM (Least Common Multiple) is the smallest positive number that is a multiple of all given numbers.

Math

↵ to calculate

Common Factor Calculator — Find GCF & All Shared Factors

Free common factor calculator. Enter any set of integers separated by commas to find all common factors, the Greatest Common Factor (GCF), and least common multiple.

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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 Common Factor Calculator finds all shared whole-number divisors (factors) for two or more integers, identifies the Greatest Common Factor (GCF / GCD / HCF), and derives the Least Common Multiple (LCM).

🔢 Integers (Separated by commas)

Enter two or more positive integers

Presets:

What is Common Factor Calculator — Find GCF & All Shared Factors?

How to use it

1️⃣ Enter two or more positive integers separated by commas (e.g. '24, 36, 48').
2️⃣ Click calculate or press Enter.
3️⃣ Review the list of all shared common factors.
4️⃣ Check the highlighted Greatest Common Factor (GCF) and individual factor breakdowns for each number.

Formula

A common factor of numbers a, b, ... is any integer d such that a mod d = 0 and b mod d = 0. GCF(a, b) = max(Common Factors).

💡 See it in action — a real example

For the numbers 12 and 18: Divisors of 12 are {1, 2, 3, 4, 6, 12}. Divisors of 18 are {1, 2, 3, 6, 9, 18}. Common factors are {1, 2, 3, 6}. The Greatest Common Factor (GCF) is 6.

❓ Common questions

What is a common factor?: A common factor is a positive whole number that divides into two or more numbers completely without leaving any remainder.
What does it mean if two numbers have only 1 as a common factor?: If the only common factor between two numbers is 1 (GCF = 1), the numbers are termed 'relatively prime' or 'coprime' (such as 8 and 9).
What is the difference between GCF and LCM?: GCF is the largest number that divides evenly into all given numbers. LCM (Least Common Multiple) is the smallest positive number that is a multiple of all given numbers.