GCF Calculator
GCF calculator: find the greatest common factor (GCD) of two or three numbers and see their LCM, with the steps explained simply.
Editorial review: Farrow (pseudonym; identity and professional credentials are not disclosed). This page is for educational purposes, not professional advice.
Your inputs
Results update as you type. Nothing you enter leaves your device.
Results
- LCM
- 144
Example with the starting values
These results use the calculator's initial inputs. Change the values above to calculate your own estimate.
Inputs
- First number
- 48
- Second number
- 36
- Third number (0 to skip)
- 0
Results
- GCF
- 12
- LCM
- 144
How does the GCF Calculator work?
The greatest common factor (GCF) is the largest number that divides every input with no remainder. The Euclidean algorithm finds it: repeatedly replace (a, b) with (b, a mod b) until the remainder is 0. For 48 and 36: 48 mod 36 = 12, then 36 mod 12 = 0, so the GCF is 12.
The GCF reduces fractions to lowest terms. 36/48 divided top and bottom by 12 gives 3/4. Leave the third number at 0 to use only two.
Frequently asked questions
What is the GCF of 24 and 36?
The GCF of 24 and 36 is 12. Both numbers divide evenly by 12, and no larger number divides both.
Is GCF the same as GCD?
Yes. Greatest common factor (GCF), greatest common divisor (GCD) and highest common factor (HCF) all mean the same thing.
What if the GCF is 1?
The numbers are coprime (relatively prime). They share no factor except 1, so a fraction made from them cannot be reduced.
How do I find the GCF by prime factors?
Factor each number and multiply the primes they share, using the lowest power. 48 = 2⁴×3 and 36 = 2²×3², so the GCF is 2²×3 = 12.