Question

Among the following, a prime number is A) 91 B) 41 C) 81 D) 51​

Answer 1

Step-by-step explanation:

41 is the prime number among these numbers

Answer 2

Answer:

B) 41

Step-by-step explanation:

What is a prime number?

• Any number which can only be divided by itself or by 1 is a prime number.

        Ex. 2,3,5,7 . . .

• Let us find the prime factorizations of the given numbers.

         $91=7*13\\41=41*1\\81=3*27=3*3*3*3=3^{4}\\51=3*17$

Clearly, 41 is the prime number,

∵ The only factors of 41 are 1 and 41 itself.

• Every prime number except 2 and 3 can be written in the form 6n+1, 6n-1.

        $6(6)+1=36+1=37\\6(7)-1 =42-1 = 41\\6(8)-1=48-1=47$

• To find prime numbers above 40, the general formula is, $n^{2} + n+41$

         for n=0 ⇒ $n^{2} + n+41 = 0^{2}+0+41=41$

       

(#SPJ3)