GCF Calculator
Greatest Common Factor Tool
Understanding the Greatest Common Factor
The Greatest Common Factor is the largest number that fits evenly into every number in a set — the key to simplifying fractions and splitting quantities into the biggest possible equal groups.
Rather than listing every factor of both numbers, the Euclidean algorithm repeatedly divides and takes the remainder, converging on the GCF in just a handful of steps — even for very large numbers.
Dividing both the numerator and denominator of a fraction by their GCF is exactly how you reduce a fraction to its lowest terms, such as turning 24/36 into 2/3.
Worked Example
To find the GCF of 48 and 18 using the Euclidean algorithm: 48 = 2 × 18 + 12, then 18 = 1 × 12 + 6, then 12 = 2 × 6 + 0. The last non-zero remainder is 6, so the GCF of 48 and 18 is 6.
Key Takeaways
- The GCF never exceeds the smallest number in the set, and it's always at least 1.
- The Euclidean algorithm scales to any number of inputs, since the GCF of a whole list is just the GCF of the running result with each next number.
- A GCF of 1 means the numbers are "coprime," sharing no common factor larger than 1.
Frequently Asked Questions
- Type a positive whole number into each row.
- Click "Add Number" to include more than two numbers, or the icon to remove a row.
- Click "Calculate" to see the greatest common factor, along with every step of the Euclidean algorithm used to find it.
The Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD), is the largest positive number that divides evenly into every number in a set. For example, the GCF of 48 and 18 is 6, since 6 is the largest number that divides both 48 and 18 with no remainder.
The Euclidean algorithm finds the GCF without needing to factor either number. It repeatedly replaces the larger number with the remainder of dividing it by the smaller number, until the remainder reaches zero — at that point, the last non-zero remainder is the GCF. This is dramatically faster than listing every factor, especially for large numbers.
Yes. Add as many rows as you need — the calculator finds the GCF of the first two numbers, then finds the GCF of that result with the next number, and so on, since the GCF of a full set equals the GCF of the running result with each additional number.
The GCF is most commonly used to simplify fractions down to lowest terms — dividing both the numerator and denominator by their GCF. It's also used in problems that involve splitting quantities into the largest possible equal groups, like arranging items into identical rows and columns.
The Greatest Common Factor is only defined for positive whole numbers, so the calculator shows a clear error if any entry is zero, negative, or not a whole number.