Numbers 

we can write n² + 8n + 49 as (n² + 2 × 4 × n + 4² + 33)
( n + 4)² + 33
( n + 4)² is always a multiple of n + 4. So, 33 should be divisible by n + 4
There are 4 positive factors of 33, (1, 3, 11 and 33) Hence, 2 × 4 i.e. 8 integral values of n.