Common Factor Calculator

The Formula

Common factors are numbers that divide evenly into both given numbers. The largest among them is the Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD). Finding common factors helps in simplifying fractions, dividing items into equal groups, and solving ratio and proportion problems.

Variable Definitions

How to Use This Calculator

1. 1

   Enter two positive integers in the input fields.

2. 2

   View the list of ALL common factors shared by both numbers, sorted from smallest to largest.

3. 3

   The largest common factor is highlighted as the GCF, which is the most practically useful value.

4. 4

   Check the individual factor lists for each number to understand how the common factors are derived.

5. 5

   Use the GCF for simplifying fractions and dividing items into equal groups.

Common factors appear in the overlap of a Venn diagram. The largest common factor is the GCF.

Understanding the Concept

Common factors are numbers that divide evenly into both of the given numbers. They represent the shared divisors between two integers. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Their common factors are 1, 2, 3, 4, 6, and 12, with 12 being the greatest. Common factors are useful in simplifying fractions to their lowest terms (dividing numerator and denominator by their GCF), dividing objects into equal groups of the largest possible size, and solving problems involving ratios and proportions. Every pair of positive integers always has at least one common factor: the number 1. Numbers whose only common factor is 1 are called coprime or relatively prime, and they are especially important in number theory and cryptography.

Frequently Asked Questions

Sources & References