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

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

AP EAMCETAP EAMCET 2016

Solution:

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