Which of the following numbers are prime:
(a) 23 (b) 51 (c) 37 (d) 26

Solution:

Prime numbers are the numbers that have only two factors, that are, 1 and the number itself.

Let p be any prime number and n be a natural number such that n² is greater than or equal to p.

If p is divisible with any prime numbers less than or equal to n, then p is not prime otherwise, p is prime

(a) 5² is 25 that is greater than 23

The prime numbers less than or equal to 5 are 2, 3, and 5

23 is not divisible by any of these numbers.

So, 23 is a prime number.

(b) 8² is 64 that is greater than 51

The prime numbers less than 8 are 2, 3, 5, and 7

51 is divisible by 3

So, 51 is not a prime number.

(c) 7² is 49 that is greater than 37

The prime numbers less than or equal to 7 are 2, 3, 5, and 7

37 is not divisible by any of these numbers.

So, 37 is a prime number.

(d) 6² is 36 that is greater than 26

The prime numbers less than 6 are 2, 3, and 5

26 is divisible by 2

So, 26 is not a prime number.

Hence, the prime numbers are (a) 23, (c) 37

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Which of the following numbers are prime:
(a) 23 (b) 51 (c) 37 (d) 26

Summary:

The following numbers are prime: (a) 23, (c) 37