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Is the GCF of two even numbers always even?
Yes.
What two numbers have a gcf of 2?
There are infinitely many pair of numbers. Take any two numbers that are coprime. Double both of them. Their GCF is 2.
Is the gcf of an odd and even number always even?
No. The opposite is true: the gcf of an odd number and an even number is always odd. All the factors of an odd number are odd; or to put it another way: If a number has an even factor, the number itself must be even. Thus the only common factors between odd and even numbers must be odd.
Why is the gcf of two even numbers are always even?
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.
The GCF of an odd and even number is 17. The greater number is 51. Find the other number?
The GCF of any set of numbers implies that all numbers in the set are multiples of the GCF. The multiples of 17 are 17,34,51 etc. If the greater number is 51 (which is an odd number) then the only solution for the other number (which is even and less than 51) is 34.
