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By definition, every even number has 2 as a factor. That means that every set of even numbers will have at least 2 as a common factor. The GCF might be higher, but if it has 2 as a factor, it's even.

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8y ago
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8y ago

By definition, every even number has 2 as a factor. That means that, at a minimum, every set of even numbers will have a common factor of 2. The GCF could be higher, of course, but that common factor of 2 will always be there, making the numbers even.

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Q: Why is the gcf of any even number always even?
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Is the GCF of any two even numbers is always even?

The GCF of any two odd numbers is always odd. The GCF of any two even numbers is always even. The GCF of an odd and an even number is always odd.


Is the gcf of a odd number and an even number always even?

The GCF of an odd and even number is never even.


Is the gcf of an even number and an odd number always even?

No, it is not.


What is the GCF of 2 and any even number?

The GCF of 2 and any even number is 2.


Is the GCF of any two numbers always odd and why?

The GCF of any two odd numbers is always odd because odd numbers don't have any even factors. The GCF of any two even numbers is always even because even numbers are divisible by two and any common factors would have at least one two in common. The GCF of an even and an odd number is odd because odd numbers don't have any even factors.


Are there any 2 even numbers that the GCF is an odd number?

No not always as for example the GCF of 7 and 21 is 7


Why is The GCF of an odd number in a even number is always even?

It's not. It's always odd.


Why is the gcf of an odd number and an even number always odd?

Because odd numbers don't have any even factors so they can't have any in common.


Is the gcf of an odd or even number ALWAYS 1?

No, it is not.


Can the greatest common factor of an odd and even number always even?

The GCF of an odd and an even number must be odd since odd numbers do not have any even factors.


Why is the gcf of any two even numbers always even?

All even numbers have two as a factor. Any two even numbers have (at the least) two as a common factor. That means the GCF of any two even numbers will have two as a factor. Any number that has two as a factor is even.


Is gcf of an odd number and an even number always even?

It is NEVER even. Because no even number can be a factor of the odd number.