GCF Calculator
The GCF is the largest whole number that divides each input without a remainder.
Enter the whole numbers
Enter two or more whole numbers. The calculator finds the greatest common factor, which is the largest whole number that divides every entered value evenly.
Use GCF for simplifying fractions, splitting items into equal groups and finding the largest shared factor. If the problem asks for a common denominator or repeating schedule, you may need LCM instead.
What the greatest common factor tells you
The GCF is a shared factor. If the GCF of 24 and 36 is 12, both numbers can be divided by 12 with no remainder. No larger whole number works for both.
This result is useful because it shows the biggest common building block. For fractions, dividing numerator and denominator by the GCF gives the simplest form in one step.
For grouping problems, the GCF tells the largest equal group size that can be used without leftovers.
GCF of 18 and 24
For 24 and 36, the factors of 24 include 1, 2, 3, 4, 6, 8, 12 and 24. The factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18 and 36. The largest shared factor is 12.
If simplifying 24/36, divide both numbers by 12. The result is 2/3.
To check the result, confirm that both original numbers divide evenly by 12. Then confirm that no larger shared factor remains.
Decimals do not belong here
The most common mistake is confusing GCF with LCM. GCF is a factor, so it is not larger than the smallest input unless the inputs include zero in a special case. LCM is a multiple and is often larger.
Another mistake is stopping at a common factor that is not the greatest. That may simplify a fraction partly, but not fully.
If the fraction still has a common factor after simplification, the number you used was not the GCF.
GCF Calculator FAQ
What is the greatest common factor?
The greatest common factor is the largest whole number that divides every number in the set evenly. For 24 and 36, the GCF is 12.
It is useful when you need the biggest shared divisor.
In fraction work, the GCF gives the largest number you can divide from the top and bottom in one step. In grouping work, it gives the largest equal group size without leftovers.
How is GCF different from LCM?
GCF is the largest shared factor. LCM is the smallest shared multiple. GCF helps divide numbers down. LCM helps build numbers up to a shared multiple.
For fractions, GCF helps simplify. LCM helps find common denominators.
A quick clue is the word factor or multiple in the problem. Factor points to GCF. Multiple points to LCM.
How do I use GCF to simplify a fraction?
Find the GCF of the numerator and denominator. Divide both by that number. The fraction keeps the same value but becomes simpler.
For 24/36, the GCF is 12. Dividing both by 12 gives 2/3.
If the fraction still has a common factor afterward, you did not divide by the greatest common factor. You can still simplify again, but the GCF gets it done directly.
Can the GCF of two numbers be 1?
Yes. If two numbers share no factor other than 1, their GCF is 1. Such numbers are called relatively prime or coprime.
A GCF of 1 means the fraction is already simplified if those numbers are numerator and denominator.
Can I find GCF for more than two numbers?
Yes. The GCF of several numbers is the largest whole number that divides all of them evenly.
For 18, 30 and 42, the shared factors include 1, 2, 3 and 6. The GCF is 6.
How can I check a GCF answer?
Divide every input by the proposed GCF. Each division should have no remainder. Then check whether the reduced numbers share another common factor.
If the reduced numbers still share a factor, the original answer was common, but it was not the greatest common factor.