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Even numbers, by definition, are divisible by 2. That means that every even number has at least one 2 as a factor. If every even number has one, then any set of even numbers will have at least one 2 as a common factor. Since that number has two as a factor, it's even.

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Q: Why is the greatest common factor of two even numbers always even?
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Related questions

Is the least common multiple of two numbers always divisible by the greatest common factor of the two numbers?

Yes, the least common multiple of two numbers is always divisible by those numbers' greatest common factor.


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The greatest factor that two or more numbers have in common is known as the greatest common factor, or GCF.


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