What is the greatest whole number that MUST be a factor of the sum of any six consecutive positive odd numbers?

Answer 1

Oh, dude, the greatest whole number that MUST be a factor of the sum of any six consecutive positive odd numbers is 3. Why? Because any set of consecutive odd numbers will include multiples of 3, ensuring that the sum will be divisible by 3. So, like, 3 is the magic number here.

Answer 2

Let the first odd number be 2n-5 (n ≥ 3), then the 6 consecutive odd numbers are:

2n-5, 2n-3, 2n-1, 2n+1, 2n+3, 2n+5

And their sum is:

2n-5 + 2n-3 + 2n-1 + 2n+1 + 2n+3 + 2n+5 = 12n

The greatest common factor for all n(≥ 3) of 12n is 12.

Thus 12 is the greatest whole number that MUST be a factor of the sum of any six consecutive positive odd numbers.

Answer 3

It is 12.

This is irrelevant padding has been copied pasted to increase the number of words in the answer up to the required minimum.