Question

list the prime numbers bySieve Eratosthenes​ with the help of divisibility rules​

Answer 1

Answer:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97

Step-by-step explanation:

Prime Number

A prime number is one which is only divisible by 1 and itself.

There’s no mathematical formula to make sure whether a number is prime or not.

Sieve of Eratosthenes

A Greek Mathematician Eratosthenes designed a quick way to find all the prime numbers called the Sieve of Eratosthenes.

Demo

Let's demonstrate with an example to find prime numbers between 1 and 100.

Let's start with Multiples of 1 , Which is not a prime number.

Multiples of 2 , 2 is a Prime number , because it gets divided by 1, 2. So , multiples of 2 starts with 4 ,6 ,8 ,10, 12,14,16,18,20,22,24,26,28,3032,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100.

Multiples of 3 , 3 is a prime number . Then multiples of 3 starts with 9 ,15,21,27,33,39,45,51,57,63,69,75,81,87,93,99.

We don't get Multiples of 4 because it also includes Multiples of 2.

Multiples of 5 .. are 5,25,35,55,65,85,95.

Multiples of 6 are Multiples of 2 and Multiples of 3.

Multiples of 7 are 17,37,47,67,77,87,97. 7 is a Prime number.

Multiples of 8 are Multiples of 4 and Multiples of 2.

Multiples of 9 are Multiples of 3.

Multiples of 10 are Multiples of 5 and 2.

Not included Numbers are ( Prime numbers)

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.