Question

Write all Prime numbers between 70 and 90.

Answer 1

Hint: Try to recall the definition of prime numbers and check all the numbers between 70 and 90 that are prime or not. If you want you can skip the even numbers, as the only even prime is 2 and no other even numbers can be prime.

Complete step by step answer:
Before moving to the solution, let us talk about the definitions of Prime numbers. The numbers which are divisible by 1 and the number itself, and has no other factors are called primes. For example: 3, 4 etc.
Now we are asked the prime numbers lying between 70 and 90. Also, we know that the only even prime is 2. So, we will check all the odd numbers between 70 and 90 one by one to check if they are prime or not.
Let us start with 71. 71 is not divisible by 3, 5 and 7. Also, it doesn’t occur in the tables of 11, 13 , 17, 19, so it is not divisible by them as well. Also, it is not divisible by any other number less than 71. So, it has no factors other than 1 and 71, so it is a Prime. Similarly, we can say 73 is also a prime.
Now let us move to 75, as the last digit of 75 is 5, it is for sure divisible by 5. So, it is not a prime. Next is 77 which is divisible by 7 and 11, so it is not prime.
However, 79 has no factors other than 79 and 1, so it is a prime. Next is 81, which is a perfect square, so it is not a prime. 83 is a prime and can be checked as we did for other primes above. 85 cannot be prime, because it is divisible by 5. Next prime number in the list is 89 and 87 is not a prime as it is divisible by 3.
So, the prime numbers lying between 70 and 90 are 71, 73, 77, 79, 83 and 89. So, there are a total of 6 prime numbers.

Note: For the problems related to prime numbers, there are no tricks or a fixed method to get the answer. You need to manually check one by one and confirm whether a number is a prime or not. However, some properties like “even numbers except 2 are never primes” may reduce your task by some extent. In addition to this you can also avoid those numbers which have 5 or 0 as their unit digit, as the numbers ending with 0 or 5 are always divisible by 5.