Question

Find out if the given number is prime or not?
89

Answer 1

Hint: Prime Numbers: Prime numbers are numbers that have only 2 factors: 1 and themselves. In other words, a number that is divisible only by itself and 1 is a prime number.

Complete step-by-step answer:
To check whether 89 is a prime number or not, we follow the following steps:
Step 1: Check whether the given number is divisible by 2 - Unit’s place of the number is 9, it is not a factor of 2. Hence, the number 89 is not divisible by 2.
Step 2: Check whether the given number is divisible by 3 - We take the sum of the digits of the number which is $8+9=17$.
The sum 17 is not divisible by 3, thus 89 is not divisible by 3.
Step 3: Since the number is not divisible by both 2 and 3, we find the square root of the given number, which is $\sqrt{89}$ which is approximately equal to 9.4
Step 4: We divide the given number by all the prime numbers below its square root value. So, we divide 89 by 7, 5, 3 and 2.
Step 5: The number 89 is not divisible by any of these numbers.
Hence, we conclude that 89 is a prime number.

Note: In this type of questions, we need to first check the divisibility of the given number by 2 and 3. If the number is divisible by any one of them, we conclude that it is not prime. If it is not divisible by any one of them, we take its square root and check its divisibility by all the prime numbers below its square root value. If it is not divisible by any of the prime numbers below its square root value, we conclude that it is prime.