Question

How many prime numbers are there between 10 and 30? Choose the correct option:
A. 6
B. 5
C. 7
D. 8

Answer 1

Hint: Check for all the numbers that have one and the number itself as the factors in order to get the prime numbers between 10 and 30.

Complete step by step solution:
In the question, we have to find the prime numbers that are between 10 and 30. So here it is well known that the prime numbers have just two factors. The two factors are the number one and the number itself. So, we will start with the number 10, and we see that it has three factors, i.e., 1, 2, 5, 10. So this is not a prime number.
Next, 11 has just two factors, i.e., 1, 11. So it is a prime number.
Next, 12 has the following factors, i.e., 1, 2, 3, 4, 12. So it is not a prime number.
Next, 13 has just two factors, i.e., 1, 13. So it is a prime number.
Next, 14 has the following factors, i.e., 1, 2, 7, 14. So it is not a prime number.
Next, 15 has the following factors, i.e., 1, 3, 5, 15. So it is not a prime number.
Next, 16 has the following factors, i.e., 1, 2, 4, 8, 16. So it is not a prime number.
Next, 17 has just two factors, i.e., 1, 17. So it is a prime number.
Next, 18 has the following factors, i.e., 1, 2, 3, 6, 9, 18. So it is not a prime number.
Next, 19 has just two factors, i.e., 1, 19. So it is a prime number.
Next, 20 has the following factors, i.e., 1, 2, 4, 5, 10, 20. So it is not a prime number.
Next, 21 has the following factors, i.e., 1, 3, 7, 21. So it is not a prime number.
Next, 22 has the following factors, i.e., 1, 2, 11, 22. So it is not a prime number.
Next, 23 has just two factors, i.e., 1, 23. So it is a prime number.
Next, 24 has the following factors, i.e., 1, 2, 3, 4, 6, 8, 12, 24. So it is not a prime number.
Next, 25 has the following factors, i.e., 1, 5, 25. So it is not a prime number.
Next, 26 has the following factors, i.e., 1, 2, 13, 26. So it is not a prime number.
Next, 27 has the following factors, i.e., 1, 3, 9, 27. So it is not a prime number.
Next, 28 has the following factors, i.e., 1, 2, 4, 7, 14, 28. So it is not a prime number.
Next, 29 has just two factors, i.e., 1, 29. So it is a prime number.
Next, 30 has the following factors, i.e., 1, 2, 3, 5, 6, 10, 15. So it is not a prime number.
Hence, the prime numbers between 10 and 30 are 11, 13, 17, 19, 23 and 29.
So total there are 6 prime numbers between 10 and 30. Hence option A is the correct answer.

Note: The number one is neither a prime nor a composite number. Now, here the other method could be first find the prime factorization, including 1, of each number and if we get more than two factors including one, then the number will not be a prime number.