All numbers have factors. Some numbers have some of the same factors as other numbers. These are common factors.
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A factor or a divisor.
Common multiples and common denominators can be found using the same process. They differ in their function. Common denominators are common multiples that are functioning as denominators.
Common denominators are common multiples that are being used as denominators.
The greatest common factor is the largest of the common factors.
Common denominators are created by finding the common multiples of unlike denominators.