Greatest Common Factor Calculator (GCF or GCD)

Written by:

On this page is a greatest common factor calculator, often abbreviated as GCF. This term goes by many names – it is also known as the greatest common divisor (GCD) and highest common factor (HCF).

Enter a set of numbers and the GCF tool will return the greatest common factor. While the tool will accept negatives and decimals, you should use positive integers.

Looking for a similar tool? Try one of these instead:

Greatest Common Factor (GCF) Calculator

What is the Greatest Common Factor (GCF) or Greatest Common Divisor (GCD)?

The Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) of a set of positive integers is the biggest positive integer which can evenly divide each number. That is: it is a positive number which can divide each number in the set and leave an integer.

Finding the Greatest Common Factor

By hand, you can find the greatest common denominator by finding each number's prime factorization – that is, the prime numbers which when multiplied together make up the number.

For example, let's use the numbers in the calculator: 14, 21, 49, and 70:

14: 2*\raisebox{.5pt}{\textcircled{\raisebox{-.9pt} {7}}}\\21:3*\raisebox{.5pt}{\textcircled{\raisebox{-.9pt} {7}}}\\49: 7*\raisebox{.5pt}{\textcircled{\raisebox{-.9pt} {7}}}\\70:2*5*\raisebox{.5pt}{\textcircled{\raisebox{-.9pt} {7}}}

And as you can see above, the largest factor that appears for all four is 7.

Using the Greatest Common Factor Calculator

In the text box at the top, enter a list of numbers where you'd like us to find the greatest common factor. You can enter whole numbers, fractions, negatives, and decimals – but it makes the most sense to enter positive integers.

When done, hit the Compute GCF button. We'll return both the Greatest Common Factor we calculate, plus the number of input numbers we understood for you to check the work.

Like this? Visit our other calculators and tools. See also our factor calculator and prime factorization calculator.

Don't Quit Your Day Job...

DQYDJ may be compensated by our advertising and affiliate partners if you make purchases through links. See our disclosures page for more information.
Sign Up For Emails
© 2009-2020 dqydj.com
linkedin facebook pinterest youtube rss twitter instagram facebook-blank rss-blank linkedin-blank pinterest youtube twitter instagram