Yes.
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Yes because if it is even then all of it's factors will be even. It is fairly different if it's an odd number. But I will not get into that.
The sum of two even numbers is always an even number.
There are infinitely many pair of numbers. Take any two numbers that are coprime. Double both of them. Their GCF is 2.
That is not possible; adding two even numbers always gives an even number
Always.