Question

Product of any $r$ consecutive natural numbers is always divisible by

• A. $r!$
• B. $(r+4)!$
• C. $(r+1)!$
• D. $(r+2)!$

Answer 1

The correct option is A $r!$

The product of $n$ consecutive natural numbers,
$(n+1)(n+2)\dots (n+r)=\frac{(n+r)!}{n!}{=}^{n+r}{C}_r\cdot r!$
Hence, it is always divisible by $r!$.