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Can you always find a third factor for larger even numbers?
Yes. An even number will always have as it's factors, itself, 1, 2 and another number. So the minimum number of factors for an even number other than 2 is four.
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.
Are the factors of an odd number always odd?
Yes. An even number is defined as being evenly divisible by 2 (no fractional answers, only integers). If an odd number has an even factor, then because of the above definition, this odd number must have a factor of 2. But you will be hard pressed to find an odd number that is a multiple of 2, because that is already the definition of an even number. So, odd numbers cannot have even factors and thus odd numbers always have odd factors.
Is an even number plus an even number always even?
Yes, an even number plus an even number is always even. Also, and odd number plus an odd number is always even.
What happens when you add an odd number and an odd number?
Two odd numbers always sum to an even number. Always. Two even numbers always sum to an even number, and an odd number and an even number always sum to an odd number.
