Question

The number 10 has four factors:1, 2, 5 and 10. The table below lists the number of factors for some numbers.

Number	Number of factors
21	4
23	2
25	3
27	4
29	2

From this, we can say that the number of prime numbers between 20 and 30 is
A. 0
B. 22
C. 3
D. 4

Answer 1

Hint: First of all, it is known that the numbers with only two factors are prime numbers. We can also say that the numbers which are not composite are known as prime numbers. Hence, find out the prime numbers from 21 to 30 that is, the numbers with only 2 factors.

Complete step by step solution:
There are 9 numbers between 20 and 30.
21, 22, 23, 24, 25, 26, 27, 28, 29, 30 lies between 20 and 30.
Here, there are 4 even numbers and 5 odd numbers.
The even numbers are 22, 24,26 and 28. The only even prime number is 2. Hence, even numbers between 20 and 30 cannot be prime.
We are given the table showing the number of factors each odd number has between 20 and 30.
Also, we know that a prime number has only two factors, the number 1 and the number itself.
Therefore, select the numbers from the table which have only two factors.
As we can see from the table, 23 and 29 have only 2 factors. So, these are prime numbers between 20 and 30.
Hence, the number of prime numbers between 20 and 30 is 2.

Note: The number of factors of a number indicates whether the number is prime or not. Many students take all the odd numbers as prime numbers which are incorrect. As from the given table, we can see that the number 21 is odd but has 4 factors and hence it is not prime.