Question

How to find that what are the prime numbers between 30 and 50?

Answer 1

Try to factorize the numbers from 30 onwards till 50.
Since 50 is between 7² and 8², it is enough to find factors less than or equal to 7.

So check for 30, 31, 32, 33, ...., 50 :  if 2,3, 5, 7 are factors of that number.

30 , 32, 34 are even numbers. So obviously they are not prime numbers.

So check for 31, 33, 35, 37, 39 ,...., 45, 47, 49  : if they have factors from 2, 3, 5, 7.  

If the numbers do not have those factors, then they are prime numbers.

Answer:   31, 37, 41, 43, 47 are prime numbers.

Answer 2

By prime table
Make elements 30 to 50
Strike multiples of 2,3,5,7,9, 11,13,15,17,19,21,23,25,29.......,and
The you will get
Prime numbers
31 37 41 43*47