About the GCF calculator
The greatest common factor (GCF), also called the greatest common divisor (GCD) or highest common factor (HCF), is the largest whole number that divides every number in your list without a remainder. This calculator finds it for two or more numbers and shows the steps of Euclid's algorithm.
It also reports the LCM and tells you when the numbers are relatively prime.
Who should use the GCF calculator
- Students simplifying fractions.
- Anyone splitting items into equal groups.
- Teachers demonstrating Euclid's algorithm.
How to use the GCF calculator: what each input means
- Numbers
- Two or more whole numbers separated by commas, spaces or new lines.
How the GCF calculator works: method and formula
Euclid's algorithm repeatedly replaces the larger number by the remainder of dividing the larger by the smaller until the remainder is zero. The last non-zero remainder is the GCF. For a list, the process is repeated with the running result and each next number.
- Euclid
- GCF(a, b) = GCF(b, a mod b), ending when the remainder is 0
How to read your GCF calculator result
A GCF of 1 means the numbers are coprime. To simplify a fraction, divide its numerator and denominator by their GCF.
GCF Calculator worked example
Find the GCF of 16, 88 and 104.
- Euclid for 88 and 16: 88 = 16 × 5 + 8
- Euclid for 88 and 16: 16 = 8 × 2 + 0
- The GCF of 88 and 16 is 8; then GCF(8, 104) = 8.
GCF(16, 88, 104) = 8.
Practical uses of the GCF calculator
- Reducing fractions to lowest terms.
- Dividing quantities into the largest equal groups.
- Finding the largest tile that fits a floor of given dimensions.
Assumptions and limitations of this calculator
- Whole numbers only, with at most 100 numbers of up to 150 digits.
- GCF of numbers that are all zero is undefined.