Question

The greatest positive integer which divides \(n(n+1)(n+2)(n+3)\) for all \(n\in\mathbb{N}\), is:

• A. \(2\)
• B. \(6\)
• C. \(24\)
• D. \(120\)

Hint:

Product of four consecutive integers is always divisible by \(4!\).

Answer 1

The Correct Option is C

Step 1: Among four consecutive integers, one is divisible by 4, one by 3, and at least two are even.
Step 2: Hence product is always divisible by \(4\times3\times2=24\).