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BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Basics of Mathematics

BITSAT 2014 · Mathematics · Basics of Mathematics

The greatest positive integer, which divides n(n+1)(n+2)(n+3) for...

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

Options

  1. A2
  2. B6
  3. C24
  4. D120

Correct answer

C. 24

Step-by-step solution

The product of r\mathrm{r} consecutive integers is divisible byr!. Thus n(n+1)(n+2)(n+3)n(n+1)(n+2)(n+3) is divisible by 4!=244 !=24
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