Prove that the product of any m consecutive integers is divisible by m.

Let all natural numbers be grouped as :

{1,2,3,.............m-1,m},{m+1,m+2,m+3,................2m},{2m+1,2m+2,2m+3,...................3m},{3m+1,3m+2,............3m}

If the sequence of m consecutive integers begin with 1,evidently the product contains m as a factor and hence is divisible by m.
Every other string of m consecutive integers starting with 2 or 3 etc. up to m contains m as a factor and hence is divisible by m.
If the sequence of m consecutive integers starting with 2m+1 or 2m+2 upto 2m contains 2m as a factor and hence is divisible by m.
The argument is similar for every other strings of m consecutive integers.

Hence,this proves that the product of any m consecutive integers is divisible by m.

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