Write the set of all prime numbers between $20$ and $50$ .

Hint: To solve the question we need to know about the prime numbers. A number is said to be a prime number if the number is divisible by one and the number itself then the number is a prime number. We will check for the divisibility of the numbers in between them and classify the number as a group of prime numbers.

Complete step by step answer:
The question asks us what are the prime numbers between $20$ and $50$. Prime numbers are exactly two factors which are one and number itself, so numbers given in the set are starting from $21$ . Since a prime number has only two factors, all the even numbers will not be prime numbers as it will also have $2$ as one of its factors. Now moving to the odd numbers we see that $21$ also has a factor $3$, so it is also not a prime number. Checking the odd numbers like this we see that the numbers which are divisible just by the number itself and one are $23,29,31,37,41,43$ and $47$.
$\therefore $ The set of numbers which are prime between $20$ and $50$ are $23,29,31,37,41,43$ and $47$.

Note: A prime number is a natural number greater than one that is not a product of two smaller natural numbers a natural number greater than one that is not a prime number is called a composite number in other words prime number is only divisible by $1$ and the number itself. Do remember that the only even number which is a prime number is $2$.