HCF Calculator
Find the Highest Common Factor of two or more numbers instantly — with full step-by-step working, factor lists, prime factorization, and the Euclidean Algorithm all shown below your result.
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HCF (Highest Common Factor) is the largest 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 | HCF | 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 |
| HCF | GCF | |
|---|---|---|
| Full name | Highest Common Factor | Greatest Common Factor |
| Used in | UK, India, Australia | United States |
| Same answer? | Yes | Yes — always identical |
| Same methods? | Yes | Yes — identical calculation |
Frequently Asked Questions
What is the HCF?+
HCF stands for Highest Common Factor. It is the largest number that divides evenly into all the numbers you give it. For example, the HCF of 12 and 18 is 6, because 6 is the biggest number that fits perfectly into both 12 and 18.
Is HCF the same as GCF?+
Yes, exactly the same. HCF (Highest Common Factor) is used mainly in the UK, India, and Australia. GCF (Greatest Common Factor) is used more in the United States. Both mean the same thing and are found using the same methods.
What is the HCF of two prime numbers?+
Always 1. Prime numbers only have two factors: 1 and themselves. Since two different prime numbers do not share themselves as a factor, the only shared factor is 1.
Can the HCF be larger than one of the numbers?+
No. The HCF can never exceed the smallest number in the group. A number cannot be divided evenly by any number larger than itself (except in trivial cases with 0).
What does HCF = 1 mean?+
It means the numbers are co-prime (also called relatively prime). They share no common factors other than 1. For example, 8 and 15 have an HCF of 1 even though neither is prime.
What is the HCF of a number and 0?+
By convention, HCF(n, 0) = n. This is because every number divides 0 (0 = n × 0), so the highest common factor is n itself.
How do you find HCF quickly for large numbers?+
Use the Euclidean Algorithm. Divide the larger number by the smaller, then replace the larger with the smaller and the smaller with the remainder. Repeat until the remainder is 0. The last non-zero remainder is the HCF.
Where is HCF used in real life?+
HCF is used to simplify fractions (divide top and bottom by the HCF), to split objects into equal groups with no leftovers, to find the largest square tile that fits a rectangular floor exactly, and in music theory to find common rhythmic denominators.