Complete guide
GCF calculator with Euclidean steps and reduced ratio
Paste 2 to 20 integers. Calculator24 returns their greatest common factor, reduced ratio, common divisors and the successive Euclidean steps.
What GCF means
The greatest common factor, also called greatest common divisor, is the largest positive integer that divides every input without remainder.
Euclidean algorithm
Divide and keep the remainder. Replace the pair with the divisor and remainder until the remainder is zero.
GCD(a,b)=GCD(b,a mod b)More than two integers
Find the GCF of the first pair, then combine that result with each remaining input.
Worked ratio example
84, 126 and 210 share 42. Dividing every term by 42 yields the simplest whole-number ratio 2:3:5.
Zeros and signs
Absolute values determine divisibility. GCD(a,0)=|a|, while an all-zero list has no positive greatest divisor in this tool.
Uses of a common factor
GCF reduces fractions and ratios, groups objects into equal largest sets and factors common coefficients from expressions.
Euclidean example for 126 and 84
| Division | Quotient | Remainder |
|---|---|---|
| 126÷84 | 1 | 42 |
| 84÷42 | 2 | 0 |
| Result | GCF 42 |
Frequently asked questions
Is GCF the same as GCD?
Yes for integers.
What is the GCF of 84 and 126?
It is 42.
Can the GCF be negative?
No. This page reports the conventional nonnegative divisor.
Can I include zero?
Yes, provided at least one number is nonzero.
How does GCF reduce a ratio?
Divide every term by the shared GCF.
Can I enter decimals?
No. GCF is defined here for whole integers.
What to keep in mind
Signs are ignored and zeros are supported when at least one input is nonzero. Each absolute value must be at most one trillion; enter 2 to 20 integers.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.