Question

Find the number of prime numbers between \[20\] and \[40\], both inclusive.

Answer 1

Hint: prime numbers are the positive integers, those numbers are having only two factors, 1 and the integer itself. Prime numbers cannot have other factors other than, 1 and the integer itself.
The numbers having other factors along with 1 and itself, those numbers are called composite numbers.

Complete step-by-step answer:
From the question it is clear that we have to find the number of prime numbers between \[20\] and \[40\], both inclusive.
In mathematics, prime numbers are the natural numbers and also positive integers.
prime numbers are having only two factors, 1 and the integer itself. Prime numbers cannot have other factors other than, 1 and the integer itself.
The numbers having other factors along with 1 and itself, those numbers are called composite numbers.
Let us try to write all the numbers between \[20\] and \[40\], both inclusive.
\[20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40\].
So, these are the numbers between \[20\] and \[40\].
Observe these numbers carefully, we can see only
\[23,29,31,37\] are the four numbers that do not have factors other than 1 and itself.
Since these numbers \[23,29,31,37\]are divisible by themselves and 1, they are prime numbers.
Other numbers except \[23,29,31,37\]in the list of numbers between \[20\] and \[40\], are all considered as composite numbers because they are having other factors along with 1 and itself.
Now we can conclude that there are four prime numbers between\[20\] and \[40\], both inclusive.

Note: Students should have more conceptual knowledge about prime numbers and composite numbers. conceptual error may lead to this solution wrong.