A positive integer is said to be prime if it is not divisible by any positive integer other than itself and one. Let K be a prime number strictly greater than 5 . When $$K^2+19$$​is divided by 12, the remainder will be:

Correct option is A

Given:

k is a prime number greater than 5

Formula Used:

Prime number is a number having factor as itself and 1

Solution:

If k is greater than 5 then prime numbers above 5 are 7,11,13…

​$$\frac{k^2+19}{12}$$​then remainder will be:

Let k be 7

​$$\frac{7^2+19}{12} = \frac{68}{12}$$​ Remainder is 8

If k is 11

Then $$\frac{11^2+19}{12} = \frac{140}{12}$$ Reaminder is 8

Hence the answer is 8