If you take any three whole numbers A, B and C and calculate the differences A-B, A-C and B-C, and then multiply those three differences together you can prove that the result will always be even. This is because of the numbers A, B and C, either at least two of them are even, or at least two of them are odd, and so at least one of the differences must be even.

If instead you consider a set of any 6 whole numbers A-F and do the same thing, what is the highest number that the resulting product will definitely be divisible by?

Just to be clear, the difference between every pair of numbers is considered, but only one way, so (A-B) would be included but not also (B-A).