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

Solution:

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

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.

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

Summary:

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