Question

How do you list all the prime numbers between \[80\] and \[90\]?

Answer 1

Hint: From the question, we have been asked to list all the prime numbers between \[80\] and \[90\].First of all, we have to know about the definition of a prime number. Prime number: A number that is divisible only by itself and one.

Complete step-by-step solution:
From the question, we have been asked to list all the prime numbers between \[80\] and \[90\].
We can remove the even numbers in between \[80\text{ and 90}\] because the even numbers are the numbers which are divisible by \[2\]. So, they cannot be the prime numbers.
Now, we have to verify the remaining numbers in the list.
First of all, let us verify the number \[81\].
\[81\] Can be divisible by \[3\] because the sum of the digits is \[9\] which is divisible by \[3\].
So, it is not a prime number.
Now, let us verify the number \[83\].
\[83\] Is not divisible by \[3\] and \[7\]. We don't have to test any further.
Therefore, it is a prime number.
Now, let us verify the number \[85\].
We can clearly observe that \[85\] is a multiple of \[5\] because the unit digit is \[5\].
Therefore, it is not a prime number.
Now, let us verify the number \[87\].
\[87\] Can be divisible by \[3\] because the sum of digits is \[15\] which is divisible by \[3\].
Now, let us verify the number \[89\].
\[89\] Cannot be divisible by \[3\] and \[7\]. We don't have to test any further.
Therefore, it is a prime number.
Therefore, \[83\text{ and 89}\] are the only two prime numbers between \[80\text{ and 90}\].


Note: We should be very careful while identifying the prime numbers. First of all, we should know the definition of a prime number. Also, we should be very careful while doing the divisibility checking for every number. Every number is to be checked correctly whether it is divisible by any number or not. We should be careful while checking the divisibility of the numbers. Sometimes I suggest it’s better for us to remember all prime numbers between $1$ to $100$ because we have very less around $25$ and that would be helpful for us.