How it works
Calculate the Greatest Common Factor (GCF/GCD) of two or more numbers.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
1-
?numbers=Enter numbers (comma separated)Text · Optional · Default: 24, 36, 48
Outputs
1-
resultResultText · Primary output
result contains the calculator’s complete rendered result area, including its visible result cards, tables, charts, and messages.
Find the largest number that divides a set of integers
Description
The Greatest Common Factor (GCF) Calculator—also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) tool—identifies the largest positive integer that divides each of the numbers in a given set without leaving a remainder. This calculation is a fundamental step in simplifying fractions, find common denominators, and solving various algebraic problems.
Inputs
- Numbers: A list of two or more integers separated by commas or spaces (e.g.,
24, 36, 48).
Outputs
- GCF: The largest shared divisor for the entire set of numbers.
Chart
- N/A: This tool provides a direct numeric result.
“Good to Know”
- Simplifying Fractions: To reduce a fraction to its simplest form, find the GCF of the numerator and denominator and divide both by that number.
- Euclidean Algorithm: This calculator uses an efficient recursive method called the Euclidean Algorithm to find the GCF, which works even for very large numbers.
- Relatively Prime: If the GCF of two numbers is 1, those numbers are “relatively prime.”
Examples
Example 1: Basic Pair
- Input:
24, 36 - Output: 12
Example 2: Multiple Numbers
- Input:
12, 18, 24 - Output: 6
Example 3: Coprime Set
- Input:
7, 13 - Output: 1