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Q: What is the greatest common factor that the sum of any 17 consecutive counting numbers must possess?
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What is the greatest common factor that the sum of any 3 consecutive counting numbers must possess?

I think I know what you're asking, but it doesn't work like that. The sum of any set of numbers is a single number and single numbers don't have common factors until they are compared to at least one other number. The sum of three consecutive counting numbers will be at least a multiple of 3.


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Every natural number has factors. A factor is any number that will evenly (or wholly) divide the first number leaving no "remainder". So 5 is a factor of 10, because 10 divided by 5 is exactly 2 with nothing left over. A "common factor" is any factor that two or more numbers share in common. So 8 and 12 have a common factor of 4, that is, they both have 4 as a factor. The numbers, 24, 18, 15, and 21 possess a common factor of 3. The "greatest common factor" is the largest such factor that two numbers share in common. For example: given the two numbers 12 and 6, which have common factors of 1, 2, 3, 4 and 6, the greatest (or 'highest') common factor is 6. NOTE: A single number in itself cannot have a "common" factor, even though, as stated, it has factors of itself. The term "common" means that more than one number must be involved so that a comparison of factors can be made between the numbers to see what factor is common to all/both.


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