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Q: Why cant two even numbers have a gcf of 1?

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Two even numbers won't have an odd GCF.

The GCF of two even numbers is 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.

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.

The GCF of two even numbers is always even.

No. If both numbers are even, their GCF must be even itself.

All even numbers have two as a factor. Since two will be a common factor of any set of even numbers, the GCF will also have two as a factor, making it even.

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.

Any consecutive even numbers have a GCF of 2.

The GCF is 2.

If one of the numbers is a multiple of the other, the smaller number is the GCF. If the two numbers are prime numbers, the GCF is 1. If the numbers are consecutive, the GCF is 1. If the numbers are consecutive even numbers, the GCF is 2.

It will be an even number.

No. For example, the GCF of 8 and 12 is 4. The GCF of 12 and 18 is 6. The Greatest Common Factor of two even numbers will always be even, but it will not always be 2.

no

No

Yes, two even numbers will have an even GCF.

That is correct.

Yes.

Yes.

No. The GCF of 4 and 8 is 4.

No. The GCF of 8 and 12 is 4.

Not always. The GCF of 8 and 12 is 4.

Yes.

There's a lot of possibilities. Any set of consecutive even numbers has a GCF of 2.

True. Even numbers are even because they are multiples of 2. That means that any two even numbers will have at least 2 as a common factor. Since that number (the GCF) will have 2 as a factor, it will be a multiple of 2: an even number.