Find the remainder when the square of any prime number greater than 3

1.	Find the remainder when the square of any prime number greater than 3 is divided by 6. A) 6 B) 7 C) 9 D) 1
Answer» Correct option is (D) 1 Any prime number greater than 3 is of the form \(6k\pm1,\) where k is a natural number. Thus, \((6k\pm1)^2\) \(=36k^2\pm12k+1\) = 6k (6k \(\pm\) 2) + 1 When \((6k\pm1)^2\) or (6k (6k \(\pm\) 2) + 1) is divided by 6, we get k (6k \(\pm\) 2) as a quotient and 1 as a remainder. \(\therefore\) When the square of any prime number greater than 3 is divided by 6, we get 1 as a remainder. Correct option is D) 1

Find the remainder when the square of any prime number greater than 3 is divided by 6. A) 6 B) 7 C) 9 D) 1

Answer»

Correct option is (D) 1

Any prime number greater than 3 is of the form \(6k\pm1,\) where k is a natural number.

Thus, \((6k\pm1)^2\) \(=36k^2\pm12k+1\)

= 6k (6k \(\pm\) 2) + 1

When \((6k\pm1)^2\) or (6k (6k \(\pm\) 2) + 1) is divided by 6, we get k (6k \(\pm\) 2) as a quotient and 1 as a remainder.

\(\therefore\) When the square of any prime number greater than 3 is divided by 6, we get 1 as a remainder.

Correct option is D) 1