The greatest positive integer which divides (n+16)(n+17)(n+18)(n+19), for all positive integers n, is

Question

The greatest positive integer which divides (n+16)(n+17)(n+18)(n+19), for all positive integers n, is (A) 6 (B) 24 (C) 28 (D) 20

Tardigrade Admin · Accepted Answer

We have, (n+16)(n+17)(n+18)(n+19) These numbers are the product of four consecutive natural numbers. ∴ This number divides by 4 !=24.

Q. The greatest positive integer which divides $(n + 16) (n + 17) (n + 18) (n + 19)$ , for all positive integers $n$ , is