GCF Calculator
Use this free GCF Calculator to calculate your Greatest common factor instantly and accurately.
Numbers
GCF result
What is a GCF Calculator?
A GCF calculator finds the greatest common factor (also called greatest common divisor) of two or more numbers. This is the largest number that divides evenly into all of them. Students use it for simplifying fractions, teachers use it for checking homework, and anyone splitting quantities into equal groups finds it useful. The calculator above also shows the least common multiple (LCM) and the full list of common factors.
How to find the GCF manually (the formula)
There are three methods to find the GCF by hand:
Listing factors: Write down every factor of each number, then pick the largest one they share. For 12 and 18: factors of 12 are 1,2,3,4,6,12; factors of 18 are 1,2,3,6,9,18. The GCF is 6.
Prime factorisation: Break each number into its prime factors, find the common primes, and multiply them together. 12 = 2² × 3, 18 = 2 × 3². Common primes are 2 and 3, so GCF = 2 × 3 = 6.
Euclidean algorithm: Divide the larger number by the smaller, then replace the larger with the remainder and repeat until the remainder is zero. The last non-zero remainder is the GCF. This is the fastest method for large numbers.
Example calculation
Find the GCF of 48, 60, and 72.
Step 1: Find prime factors: 48 = 2&sup4; × 3, 60 = 2² × 3 × 5, 72 = 2³ × 3²
Step 2: Identify common primes: 2 and 3 appear in all three
Step 3: Take the smallest exponent for each: 2² and 3¹
Step 4: Multiply: 4 × 3 = 12
Step 5: Check: 48 ÷ 12 = 4, 60 ÷ 12 = 5, 72 ÷ 12 = 6. All whole numbers.
The GCF of 48, 60, and 72 is 12.
Common mistakes
- Confusing GCF with LCM — GCF is the largest number that divides all inputs, while LCM is the smallest number all inputs divide into. They are not the same.
- Using the wrong exponent in prime factorisation — take the smallest exponent for each common prime, not the largest. The largest gives you the LCM.
- Forgetting to check all numbers — when working with three or more numbers, a factor must divide every single one. A factor of two numbers may not divide the third.
- Stopping the Euclidean algorithm too early — keep dividing until you reach zero remainder. The last non-zero remainder is the GCF.
Frequently asked questions
How do I find the GCF on a calculator?
Enter your numbers separated by commas or spaces into the calculator above and click Calculate. The tool uses the Euclidean algorithm to compute the greatest common factor instantly, including the common factors list and the LCM.
How do I find the greatest common factor by hand?
List all factors of each number, then pick the largest one they share. For 48 and 60: factors of 48 are 1,2,3,4,6,8,12,16,24,48 and factors of 60 are 1,2,3,4,5,6,10,12,15,20,30,60. The largest common factor is 12. You can also use prime factorisation or the Euclidean algorithm (repeated division) for larger numbers.
What is the difference between GCF and LCM?
GCF (greatest common factor) is the largest number that divides evenly into all given numbers. LCM (least common multiple) is the smallest number that all given numbers divide into evenly. For 12 and 18, the GCF is 6 and the LCM is 36. They are related: GCF × LCM = product of the two numbers.
What is the Euclidean algorithm for GCF?
Divide the larger number by the smaller number. Replace the larger number with the remainder and repeat until the remainder is zero. The last non-zero remainder is the GCF. For 48 and 60: 60 ÷ 48 = 1 remainder 12, then 48 ÷ 12 = 4 remainder 0, so GCF is 12.
Can you find GCF of more than two numbers?
Yes. Find the GCF of the first two numbers, then find the GCF of that result and the next number, and repeat. The calculator above supports any number of inputs separated by commas or spaces.
When would I use GCF in real life?
GCF is used for simplifying fractions, splitting items into equal groups, dividing a budget or area into the largest possible equal sections, and solving ratio and proportion problems.