A "Common Factor" of two (or more) integers is any integer that will divide into each of them. Thus a common factor of $a$ and $b$ is a divisor of each of them. By default, and by convention, we usually ask for positive common factors, but negative numbers can also be common factors.

When we work with Complex Numbers there is not concept of positive and negative.

Trivially, 1 is always a common factor of any collection of integers.

Examples:

• A common factor of 15 and 21 is 3.
• A common factor 105 and 70 is 5
• Other common factors of 105 are 7, and 35.
• A common factor of 154 and 455 is 1.
• ... and that is the only positive common factor.
When cancelling fractions we try to find a common factor of both the numerator and denominator, and then divide each by that common factor.

For two given numbers there is also a Highest Common Factor (HCF), which can be found by using the Euclidean Algorithm.

This is related to:
EquivalentFractions
Euclid
EuclideanAlgorithm
LeastCommonMultiple
ReducingFractionsToLowestTerms
ComplexConjugate
ComplexNumber
DividingComplexNumbers
SubtractingComplexNumbers
WhatIsATopic
CancellingFractions
CommonMultiple
HighestCommonFactor
MultiplyingComplexNumbers

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CommonFactor
ComplexNumber
Denominator
Divisor
EuclideanAlgorithm
Integer
Numerator
LeastCommonMultiple
ReducingFractionsToLowestTerms
ArgandDiagram
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ComplexConjugate
ComplexPlane
ContinuedFraction
DividingComplexNumbers
Euclid
Euler
ImaginaryNumber
ModuloArithmetic
MultiplyingComplexNumbers
PolarRepresentationOfAComplexNumber