How the Greatest Common Factor / Common Factors Calculator works.
gcd(a,b) = gcd(b, a mod b)The comma-, space-, or line-separated inputs are positive whole numbers; GCF, GCD, and HCF are equivalent names for the same greatest divisor.
Worked example for the Greatest Common Factor / Common Factors Calculator.
For 84 and 126, 126 mod 84 is 42 and 84 mod 42 is 0, so the greatest common factor is 42.
How to read this result.
The combined tool reports the GCF and can also list every positive factor shared by all entered integers.
How the calculation works
The Euclidean algorithm repeatedly replaces the larger integer with the remainder until the remainder is zero; the last nonzero remainder is the GCF. Formula or rule: gcd(a,b) = gcd(b, a mod b). The comma-, space-, or line-separated inputs are positive whole numbers; GCF, GCD, and HCF are equivalent names for the same greatest divisor.
What this calculator does not prove
GCF and common-factor lists describe integer divisibility. They do not simplify algebraic expressions with symbolic variables or approximate decimal measurements. Use the result for the mathematical question shown here; a correct calculation does not by itself establish that the source data, sample, or real-world assumption is appropriate.
Inputs and edge cases to check.
Enter 2–100 positive whole numbers. Decimals, signs, zero, blank list items, and values above the supported integer range are rejected.
What this tool does not include.
GCF and common-factor lists describe integer divisibility. They do not simplify algebraic expressions with symbolic variables or approximate decimal measurements.
Reference guidance and methodology.
Greatest Common Factor / Common Factors Calculator questions.
What does the Greatest Common Factor / Common Factors Calculator calculate?
Find the GCF, GCD, or HCF of several integers and optionally list every factor common to them.
Which formula or algorithm does it use?
gcd(a,b) = gcd(b, a mod b). The comma-, space-, or line-separated inputs are positive whole numbers; GCF, GCD, and HCF are equivalent names for the same greatest divisor.
What limitations or edge cases matter?
Enter 2–100 positive whole numbers. Decimals, signs, zero, blank list items, and values above the supported integer range are rejected. GCF and common-factor lists describe integer divisibility. They do not simplify algebraic expressions with symbolic variables or approximate decimal measurements.