GCF Calculator
The GCF Calculator finds the greatest common factor, also called the greatest common divisor or GCD, of two or more positive integers. The GCF is the largest positive integer that divides every number in the set without a remainder. This calculator uses repeated Euclidean reduction, a fast method that works without listing every factor first.
Separate numbers with commas or spaces. You can calculate more than two numbers at once.
The calculator repeatedly applies the Euclidean algorithm until all entered integers have been reduced to their greatest shared factor.
How to use the GCF Calculator
- Enter two or more positive integers separated by commas or spaces.
- For two numbers, the calculator divides and keeps the remainder.
- The previous divisor and remainder become the next pair.
- Euclidean division continues until the remainder reaches zero.
- The final non-zero divisor is the GCF for that pair.
- For additional numbers, the result is combined with each remaining integer.
- Use the LCM Calculator when you need the smallest shared multiple instead.
Examples
GCF of 12 and 18
The greatest number dividing both 12 and 18 is 6.
GCF of 24 and 36
Both numbers are divisible by 12, and no larger common factor exists.
GCF of 8, 12 and 20
The greatest common factor shared by all three numbers is 4.
GCF of coprime numbers
If two integers share no positive factor larger than 1, their GCF is 1.
Frequently asked questions
What does GCF mean?
GCF means greatest common factor, the largest positive integer that divides all numbers in a set exactly.
Is GCF the same as GCD?
Yes. Greatest common factor and greatest common divisor describe the same mathematical value.
What is the Euclidean algorithm?
It repeatedly replaces a pair of integers with the divisor and remainder until the remainder becomes zero.
What is the GCF of 12 and 18?
6.
Can this calculate more than two numbers?
Yes. Enter multiple positive integers separated by commas or spaces.
What does a GCF of 1 mean?
It means the entered integers have no common positive factor greater than 1 and are relatively prime as a group.
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