GCF Calculator
Find the Greatest Common Factor of two or more numbers instantly — with full step-by-step working shown.
Enter numbers
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GCF (Greatest Common Factor) is the biggest number that divides evenly into all your numbers. Enter any numbers above and the full working — factor lists, prime factorization, and Euclidean steps — will appear here automatically.
| Numbers | GCF | Why |
|---|---|---|
| 12, 18 | 6 | 6 × 2 = 12 and 6 × 3 = 18 |
| 15, 25 | 5 | Both divisible by 5 |
| 7, 13 | 1 | Both prime — co-prime |
| 24, 36 | 12 | 12 × 2 = 24 and 12 × 3 = 36 |
Frequently Asked Questions
What is the GCF?+
The Greatest Common Factor (GCF) is the biggest number that divides evenly into all the numbers you are working with. For example, the GCF of 12 and 18 is 6, because 6 is the largest number that fits perfectly into both.
What is the difference between GCF and HCF?+
Nothing! GCF (Greatest Common Factor) and HCF (Highest Common Factor) are exactly the same thing. GCF is used more in the US; HCF is used more in the UK and India.
What is the GCF of two prime numbers?+
Always 1. Prime numbers have no factors other than 1 and themselves. So two different prime numbers share only the factor 1.
Can the GCF ever be larger than both numbers?+
No. The GCF can never be larger than the smallest number in the group, because a number cannot be divided evenly by anything larger than itself.
What is the GCF of a number and 1?+
Always 1. The only factor of 1 is 1 itself, so the only factor they can share is 1.
What does it mean if the GCF is 1?+
It means the numbers are co-prime (or relatively prime). They share no common factors other than 1. Example: 8 and 9 have a GCF of 1.
How is GCF used in real life?+
GCF is used to simplify fractions (divide both numerator and denominator by the GCF), split things into equal groups without leftovers, and find the largest tile size that fits a floor perfectly.
What is the fastest method to find the GCF?+
The Euclidean Algorithm is the fastest method for large numbers. For small numbers, listing all factors and finding the biggest common one works perfectly well.
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