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.