What is the HCF?
The highest common factor is the largest whole number that divides exactly into every number in the list. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. The factors of 180 include 12 but not 16 or 24, and 84 also includes 12, so the HCF of 48, 180 and 84 is 12. UK schools say HCF, while the US says GCF or GCD.
The Euclidean algorithm
Instead of listing factors, divide the larger number by the smaller and keep the remainder, then repeat with the smaller number and the remainder until the remainder is 0. The last non-zero remainder is the HCF. It's fast even for huge numbers. Simplifying fractions uses the HCF: try the fraction calculator.
Frequently asked questions
Is HCF the same as GCF and GCD?
Yes: highest common factor, greatest common factor and greatest common divisor are all the same thing.
What is the HCF of two prime numbers?
1.
How to use the HCF (GCF) Calculator
- Enter your numbers.
- Choose the operation if needed.
- Read the answer and the working.
- Use the table below to check your understanding.
Why use this HCF (GCF) Calculator
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Nothing you enter is uploaded or stored.
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Works on phones, tablets and desktops.
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Explained
Formulas, tables and sources on the page.
HCF (GCF) Calculator: chart and reference data
Source: exact arithmetic
| Numbers | HCF (GCF) | LCM |
|---|---|---|
| 12 and 18 | 6 | 36 |
| 8 and 12 | 4 | 24 |
| 15 and 25 | 5 | 75 |
| 21 and 6 | 3 | 42 |
| 24 and 36 | 12 | 72 |
| 7 and 13 | 1 | 91 |
HCF (GCF) Calculator compared with the alternatives
| Option | Shows working | Cost | Availability |
|---|---|---|---|
| This calculator | Yes | Free | Any device |
| Scientific calculator | No | £10–£20 | Needs the device |
| Spreadsheet | With formulas | Licence or account | Needs setup |
Who uses it in the UK
- GCSE and A-level revision
- University and coursework grades
- Electronics and science labs
- Sports stats and health checks
More questions
Does it show the working?
Where it helps, yes – the result section explains the steps so you can check your homework or report.
Can I use it for GCSE or A-level revision?
Yes. It is a good way to check answers, but make sure you can do the method by hand, as calculators are not allowed in every exam paper.
How accurate is it?
It uses standard double-precision arithmetic, accurate to about 15 significant figures. Results are rounded only for display.
Is my data stored?
No. Everything is calculated in your browser.
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