How to use the greatest common factor calculator
Put two or more integers into the input, separated by commas or spaces, then select Calculate. The result shows the GCF, the Euclidean algorithm work, and a plain-text version you can copy or download.
Calculate a GCF from a list of integers
Type the values into Integers (comma or space separated). A value may have a plus or minus sign. The calculation uses its absolute value, so -18 is treated as 18.
- Enter two or more integers, such as
18, 24, 30. - Select Calculate.
- Review the GCF and the work under Formula & steps.
- Select Copy result or Download result (.txt) if you need the result elsewhere.
For those three values, the result includes:
Numbers: 18, 24, 30
GCF = 6How the GCF calculator uses the Euclidean algorithm
For each pair, the calculator applies GCF(a, b) = GCF(b, a mod b) until the remainder is zero. The last nonzero value is that pair's GCF. With more than two integers, the running GCF becomes the first value in the next pair: GCF(a, b, c) = GCF(GCF(a, b), c).
Formula & steps lists the input, the formula, each remainder, and the intermediate pair results. JavaScript BigInt arithmetic keeps the integer calculation exact within the input rules, and the result is calculated locally in your browser.
GCF calculator input rules and zero values
Enter 2 to 50 integers. Each integer may contain up to 100 digits and an optional plus or minus sign. Commas and whitespace separate values. Text, decimal values, empty input, fewer than two values, oversized integers, and more than 50 values produce an error.
At least one value must be nonzero. 0, 24 returns 24, while 0, 0 is rejected because its GCF is undefined. Reset clears the input and error, then hides the current result.
Where a greatest common factor calculation comes up
To compare 42 and 56, enter both values and get a GCF of 14. That number can be used when dividing the values into equal groups.
For a fraction, calculate the GCF of the numerator and denominator before dividing both by the result. When checking an integer routine, enter several test values and inspect each Euclidean step.
Choose the right math calculator
Browse Math Calculators for related tools. Use the Least Common Multiple Calculator for an LCM. Use the Fraction and Ratio Calculator for fraction operations, mixed numbers, ratio simplification, or proportions. The Number Theory Calculator combines several number-theory calculations.
Frequently asked questions
How do I use a GCF calculator?
Enter at least two integers in Integers (comma or space separated), select Calculate, and read the GCF under Formula & steps. Then select Copy result or Download result (.txt).
Is the greatest common divisor the same as the GCF?
Yes. Greatest common divisor and greatest common factor name the same value, the largest positive integer that divides every entered integer without a remainder.
Can I calculate the GCF of more than two numbers?
Yes. Enter up to 50 integers, separated by commas or whitespace. The calculator combines them pairwise and shows the running results.
What happens with negative numbers or zero?
Negative signs are ignored when the GCF is calculated. A zero can be combined with a nonzero integer, while an input made entirely of zeros is rejected.