Question

How many prime numbers are there between 0 and 30?
A. 9
B. 10
C. 8
D. 11

Answer 1

Hint: Recall from the definition of prime numbers that the prime numbers are the numbers with only two factors. Determine the number of factors of the numbers from 0 to 30. Then, count the numbers with only two factors which will be prime numbers.

Complete step by step Answer:

We know that the prime numbers are those numbers that have only factors.
We have to find the number of prime numbers from 0 to 30.
We will find factors for each number from 0 to 30
0 has no factor.
1 has only 1 factor, that is 1 itself. Hence, 1 is not a prime number.
The factors of 2 are 1 and 2. Thus, 2 is the prime number.
Similarly, 3 has only 2 factors, therefore, 3 is a prime number.
All the even numbers after 2 will have at least 2 has as a factor, and hence cannot be prime.
Also, the numbers 5 and 7 are divisible by 1 and by itself, thus, 5 and 7 are prime numbers.
But, 9 has factors 1,3, and 9. So, 9 is a composite number.
11 and 13 are prime numbers as they have only 2 factors.
The factors of 15 are 1, 3,5, and 15. Hence, 15 is not a prime number.
17 and 19 have only 2 factors and thus are prime numbers.
21 has factors 1,3,7 and 21. So, 21 is not a prime number.
We also know that 23 has only 2 factors. Thus, 23 is a prime number.
The factors of 25 are 1,5 and 25. Then, 25 is a composite number.
We will now write the factors of 27 which are 1,3,9 and 27.
Also, 29 has factors 1 and 29. Thus, it is a prime number.
Therefore, the prime numbers from 0 to 30 are 2,3,5,7,11,13,17,19,23 and 29
Hence, there is a total of 10 numbers from 0 to 30.
Thus, option B is the correct answer.

Note: Many students make mistakes by considering all the odd numbers as prime numbers. But, there are odd numbers with more than 2 factors. For example, 9 has factors 1,3 and 9, thus, 9 is a composite number.