The product of r consecutive positive integers is divisible by

Let r consecutive positive integers bem, m + 1, m + 2, … (m + r – 1), where m ∈ N∴  Product =m(m+1)(m+2)…(m+r−1)=(m−1)!m(m+1)(m+2)…(m+r−1)(m−1)!=(m+r−1)!(m−1)!=r!⋅(m+r−1)!r!(m−1)!=r!⋅m+r−1Crwhich is divisible by r!          (∵ m + r – 1Cr is a natural number)