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Math / Common Factor

Common Factor Calculator

List the positive common factors shared by two integers and show their greatest common factor. This makes the full shared divisor set visible instead of returning only the largest simplification factor. The shared factors are the positive divisors of gcd(|a|,|b|). Euclid’s algorithm finds the gcd, after which its divisor pairs enumerate the common set.

Your inputs

Make it your own
Calculator settings

Your result
1, 2, 3, 6
Common factors
Greatest common factor
6

Example inputs shown. Adjust them to explore.

A familiar situation

List every shared divisor when comparing two counts of objects or simplifying ratios.

How to use this calculator

  1. Enter first integer, second integer.
  2. Select Calculate to see the answer and its breakdown.
  3. Keep a scenario, change an input and compare the results.

Use consistent units and check the assumptions below before applying the result.

How common factor is calculated

The shared factors are the positive divisors of gcd(|a|,|b|). Euclid’s algorithm finds the gcd, after which its divisor pairs enumerate the common set. For 18 and 24, the common factors are 1, 2, 3, and 6; the greatest is 6.

Common factors of a and b are exactly the positive divisors of gcd(|a|,|b|).
A worked example

For 18 and 24, the common factors are 1, 2, 3, and 6; the greatest is 6.

Assumptions & useful context

The result depends on the values you enter and the method described above. Displayed numbers may be rounded; calculations use the unrounded values. Check that this model matches your situation before relying on it.

Frequently asked questions

Can values be negative?

Yes; divisibility uses absolute values.

Can both values be zero?

No; that would produce an unbounded set of common divisors.

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