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

1. 2
2. 4
3. 24
4. 120

Please give detailed answer !!!

Since it is the multiplication of four consecutive numbers, hence it will always be divisible by 4!. That is, 24 will always divide the above number irrespective of value of n.

It will also probably be the largest.