Question

How many prime numbers are less than 50?
a). 16
b). 15
c). 14
d). 18

Answer 1

Hint: To solve the question, we have to use the concept of the prime numbers condition which states a prime number has only two factors, 1 and the number itself. List down all the natural numbers below 50 and apply the divisibility rule of 2,3,5,7 to eliminate the non-prime numbers. Thus, can we obtain the list of prime numbers below 50.

Complete step-by-step answer:
The numbers below 50 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49.
A prime number is a number which has only two factors 1 and itself. Thus, we can eliminate the number 1 since it has only factor 1.
The remaining numbers below 50 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49.
Among the given numbers even numbers greater than 2 below 50 are
4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 40, 42, 44, 46, 48.
All the even numbers greater than 2 have factor 2 other than the number and 1. Thus, they cannot be termed as prime numbers.
The remaining numbers are 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49
Among the remaining numbers 9, 15, 21, 27, 33, 39 are divisible by 3.
Thus, they cannot be termed as prime numbers.
The remaining numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 45, 49
Among the remaining numbers 25, 35, 45 are divisible by 5 .
Thus, they cannot be termed as prime numbers.
The remaining numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49
Among the remaining numbers 49 is divisible by 7 .
Thus, it cannot be termed as prime number.
The remaining numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Thus, the prime numbers below 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Thus, the number of prime numbers below 50 = 16
Hence, option (a) is the right choice.

Note: The possibility of mistake can be at not applying all the divisibility rules of single digit prime numbers- 2,3,5,7 to eliminate all the factors of these numbers to narrow down them to a list of prime numbers. The other possibility of mistake can be not rechecking the remaining list of numbers for further confirmation.