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All even numbers have two as a factor. That means that any set of even numbers will have at least a two as a common factor. Since 2 will be a part of the greatest common factor, it will have to be even.

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Wiki User

8y ago
This answer is:
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Eloise Coleman

Lvl 1
1y ago
ty for
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Eloise Coleman

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1y ago
ty for the help!!
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Olivia Bell

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6mo ago
Yes thank you!
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Dominic Hughes

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6mo ago
im confused
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Wiki User

10y ago

Suppose A and B are two even numbers. Then, by definition,

A = 2*P for some integer P, and

B = 2*Q for some integer Q

So 2 is a factor of both A and B, that is it is a common factor.

Now, any common factor of A and B is, by definition, a factor of their HCF. That is, 2 is a factor of the HCF of A and B: in other words, the HCF is even.

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Senaol Ayane

Lvl 2
1y ago

it is becuase it is always even

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Q: Why is the gcf of two even numbers are always even?
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