Question

How many numbers of prime numbers are there between 301 and 320?

Answer 1

Hint: A prime number is a whole number greater than $1$ whose only factors are $1$ and itself. Numbers that have more than two factors are called composite numbers. The number $1$ is neither prime nor composite.

Complete step by step solution:
We have numbers $302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319.$
First, we will check these numbers are divisible by $2$ or not $–302, 304, 306, 308, 310, 312, 314, 316, 318$ (these numbers are not prime numbers because they are also divisible by $2$)
Now, we will check are they divisible by $3$ or not $–303, 306, 309, 312, 315, 318$ (these numbers are also not prime numbers because they are also divisible by $3$)
Now, we will check that these numbers are divisible by $5$ or not $–305, 310, 315$ (these numbers are also not prime numbers because they are divisible by $5$)
Now, we will check that these numbers are divisible by $11$ or not $–319$ (this number is also not a prime number because it is divisible by $11$)
So, finally, we are left with $307, 311, 313, 317$.

$\therefore $ There are four prime numbers between $301$ and $320$.

Note:
 There are so many methods to determine whether a number is prime or not. The simplest way to find prime numbers is by factorization method. By factorization, the factors of a number are obtained and, thus, you can easily identify a prime number. You can also use the divisibility test to find that a number is prime or not as we have done above. If the number is prime then it will not be divisible by any other number while divisibility tests except $1$ and itself.