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# Why is the gcf of two even numbers are always even?

Wiki User

2015-11-26 01:50:25

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.

Wiki User

2015-11-26 01:50:25
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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Wiki User

2014-03-17 19:17:10

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.

Senaol Ayane

Lvl 2
2022-11-30 02:40:12

it is becuase it is always even

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