Question

What is the next highest prime number after $67$ ?
A). $68$
B). $69$
C). $71$
D). $73$
E). $76$

Answer 1

Hint: We will divide all the numbers given in the option by prime numbers between $2 - 9$. And if they are divisible by any of the prime numbers then we can say the number is not a prime number. If any number is not divisible by a prime number, then it is a prime number.

Complete step-by-step solution:
The numbers $2,3,5,7$ are prime numbers and if any number less than $120$ is not divisible by any of these prime numbers from $2,3,5,7$ , then those numbers are known as prime numbers.
All the numbers given in the options are less than $120$, so we will divide all the numbers i.e., $68,69,71,73,76$ by the prime numbers $2,3,5,7$ and if any of the numbers is not divisible by prime number then the number is a prime number.
For $68$ , it is divisible by $2$, so $68$ is not a prime number.
For $69$, it is divisible by $3$ , so $69$ is not a prime number.
For $71$ , it is not divisible by any of the prime numbers, so $71$ a prime number.
For $73$ , it is not divisible by any of the prime numbers, so $73$ a prime number.
For $76$ , it is divisible by $2$ and $3$, so $76$ is not a prime number.
The prime numbers among the options are $71$ and $73$ .
But we are asked to find the next highest prime number after $67$, and that is $71$ .
The correct option is option C. $71$.

Note: The prime numbers are the numbers, which are only divisible by 1 or the number itself. Another way of defining it is a positive number or integer, which is not a product of any other two positive integers. There is no defined formula to find if a number is prime or not (except to a certain range), apart from finding its factors.