Question

Is 87 a prime number?

Answer 1

Hint: In the given question, we are supposed to find if the number 87 is prime or not. Firstly, we find the square root of the number 87. Then, we must divide the given number 87 with the prime numbers up to its square root. Lastly, if the given number 87 is divisible by any of the prime numbers up to its square root then it is not a prime number.

Complete step-by-step answer:
We are asked to find if the number 87 is prime or not. We will be solving the given question by finding out dividing the given number 87 with the prime numbers up to the value of the square root of 87. If the given number 87 is divisible by any of the prime numbers up to its square root then it is not a prime number.
The numbers which are greater than one and have exactly 2 factors are called Prime numbers.
For example: 3, 5, 7.
We need to find the square root of the number 87.
Finding the square root of 87, we get,
$\Rightarrow \sqrt{87}$
We know that the number 87 is not a perfect square.
To check whether a number is prime or not, we take the value less than or equal to the square root of the number.
We know that the nearest value of square root to $\sqrt{87}$ is 9
Following the same, we get,
$\therefore \sqrt{87}\approx 9$
Now, we must divide the given number 87 with the prime numbers up to 9.
If the given number 87 is divisible by any of the prime numbers up to 9 then it is not a prime number.
The prime numbers up to the number 9 are given by 2, 3, 5, 7.
A number is divisible by 2 if its last digit is 0, 2, 4, 6, 8.
The given number 87 ends with 7, so it is not divisible by 2
A number is divisible by 3 if its sum of all the digits is divisible by 3.
The sum of the digits of the given number 87 is given as follows,
$\Rightarrow 8+7$
Solving the above expression, we get,
$\Rightarrow 15$
The number 15 is divisible by 3. So, the number 87 is divisible by 3.
As the given number 87 is divisible by 3, it is not a prime number.
$\therefore$ 87 is not a prime number.

Note: The given question can be solved alternatively as follows,
The numbers which have only 2 factors 1 and the number itself are called Prime numbers.
The factors of 87 are 1, 3, 29, and 87.
As the given number 87 has more than two factors, it is not a prime number.