(a) 23 is a prime number;

23 = 1 × 23

23 = 23 × 1

Prime numbers are the numbers that can be divided by 1 and by number itself. So, 23 has two factors 1 and 23. It is a prime number.

(b) 51 is a composite number,

51 = 1 × 51

51 = 3 × 17

51 = 17 × 3

51 = 51 × 1

So, it has four factors, 1, 3, 17, and 51. Therefore it is a composite number not a prime number.

(c) 37 is a prime number,

37 = 1 × 37

37 = 37 × 1

Prime numbers are the numbers that can be divided by 1 and by number itself. 37 just have two factors 1 and 37. So it is a prime number.

(d) 26

26 = 1 × 26

26 = 13 × 2

26 = 2 × 13

26 = 26 × 1

It has four factors 1, 2, 13 and 26,

So, it’s not a prime number it is a composite number.