GCF Calculator
Find the greatest common factor of numbers.
Two or more whole numbers, separated by commas.
Results update as you type.
How it works
The greatest common factor of a set of numbers is the largest whole number that divides every one of them exactly, leaving no remainder. It captures the biggest chunk the numbers share, which is why it underpins reducing fractions, factoring expressions and splitting quantities into equal groups. The gcf calculator finds it for any list of whole numbers and, because the two ideas travel together, also returns the least common multiple. For 24, 36 and 60, the largest factor common to all three is 12, so the GCF is 12 while the LCM is 360. Rather than listing every factor of each number and hunting for the biggest match, the tool uses the Euclidean algorithm, which repeatedly replaces the larger number with the remainder of dividing it by the smaller until one becomes zero. That last non-zero value is the GCF, and the method stays fast even for large numbers, which is why a gcf calculator built on it handles long lists instantly by folding the result across the numbers pairwise. Students simplifying fractions, teachers setting factoring problems, and anyone dividing items into even portions turn to this gcf calculator for the largest shared divisor without trial and error.
GCF via the Euclidean algorithm: gcd(a, b) = gcd(b, a mod b)
The Euclidean algorithm rests on a simple fact: any number dividing both a and b also divides their remainder, so gcd(a, b) equals gcd(b, a mod b). Replacing the larger value with that remainder shrinks the problem without losing the common factor, and repeating until the remainder hits zero leaves the last divisor as the answer. Folding this across a list pairwise extends it to 24, 36 and 60, giving 12.
Source:Standard arithmetic
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter numbers.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Greatest common factor updates instantly as you type — no button to press.
Frequently asked questions
What is the greatest common factor used for?
Its most common job is simplifying fractions: dividing the numerator and denominator by their greatest common factor reduces the fraction to lowest terms in one step. It also helps factor algebraic expressions, split items into the largest possible equal groups, and find common measurements. Anywhere you need the biggest amount two or more quantities share, the GCF is the number that answers it directly.
Is GCF the same as HCF and GCD?
Yes, all three name the same value. Greatest Common Factor (GCF), Highest Common Factor (HCF) and Greatest Common Divisor (GCD) are interchangeable terms for the largest whole number that divides a set of numbers evenly. Textbooks in different countries favour different labels, but the calculation is identical, so a result of 12 for 24, 36 and 60 is correct whichever term your course uses.
How do I find the GCF of more than two numbers?
Find the GCF of the first two, then take the GCF of that result with the next number, and continue through the list. Because a factor common to all must be common to each pair, this pairwise approach gives the right answer. For 24, 36 and 60 the shared factor works out to 12. The calculator performs these steps automatically for any list you enter.
What is the difference between GCF and LCM?
The GCF is the largest number that divides all your values, while the least common multiple is the smallest number all your values divide into. One looks downward at shared factors, the other upward at shared multiples. For 24, 36 and 60 the GCF is 12 and the LCM is 360. They are linked: for two numbers, their product equals the GCF times the LCM.
Can I enter more than two numbers?
Yes. Enter any list of whole numbers separated by commas, and the calculator finds the factor common to all of them at once. There is no practical limit on how many you include. It works through the list pairwise, so adding more numbers can only keep the GCF the same or lower it, never raise it, since the more values that must share a factor, the smaller that factor tends to be.