Which one of the following groups of numbers, a) 2, 5, 15, 19  (b) 13, 11, 23, 31  (c) 2, 3, 5, 9  (d) 7, 17, 29, 49; includes all prime numbers?

Numbers that have only two factors, 1 and the number itself, are called prime numbers.

Answer: The group of numbers that includes all prime numbers is Option (b) 13, 11, 23, 31.

Let's identify the group with all prime numbers.

Explanation:

Let's look into the options individually

a) 2, 5, 15, 19 ------> 2, 5, 19 are prime but 15 = 3 × 5 is composite

b) 13, 11, 23, 31 ------> all are prime numbers as they have only two factors i.e, 1 and the number itself

c) 2, 3, 5, 9 --------> 2, 3, 5 are primes but 9 = 3 × 3 is composite.

d) 7, 17, 29, 49 --------> 7, 17, 29 are primes but 49 = 7 × 7 is composite.

Hence, option (b) 13, 11, 23, 31 contains all prime numbers.