Ayush Agarwal Maths

How to find Prime Numbers from 1 to 100 Easy Method......  Sieve of Eratosthenes. Round 1 : Cross out 1 because it is not a prime number. Round 2 : Encircle 2, cross out all the multiples of 2, other than 2 itself, i.e. 4, 6, 8 and so on. Round 3 : You will find that the next uncrossed number is 3. Encircle 3 and cross out all the multiples of 3, other than 3 itself. Round 4 : The next uncrossed number is 5. Encircle 5 and cross out all the multiples of 5 other than 5 itself. Round 5 : Continue this process till all the numbers in the list are either encircled or crossed out. All the encircled numbers are prime numbers. All the crossed out numbers, other than 1 are composite numbers. This method is called the Sieve of Eratosthenes.

A notes  1. A factor of a number is an exact divisor of that number. 2. 1 is a factor of every number. 3. Every number is a factor of itself. 4. Every factor is less than or equal to the given number. 5. Number of factors of a given number are finite. 6. Every multiple of a number is greater than or equal to that number. 7. The number of multiples of a given number is infinite. 8. Every number is a multiple of itself. 9.The number 1 has only one factor (i.e. itself ). 10. 1 is neither a prime nor a composite number. 11. 2 is the smallest prime number which is even. 12. Every prime number except 2 is odd. 13. If a number has 0 in the ones place then it is divisible by 10. 14. A number which has either 0 or 5 in its ones place is divisible by 5.  15. A number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place. 16. If the sum of the digits is a multiple of 3, then the number is divisible by 3. 17. 

     Important Terms in Mathematics  Perfect Number -  A number for which sum of all its factors is equal to twice the number is called a perfect number.  Prime Numbers -  The numbers other than 1 whose only factors are 1 and the number itself are called Prime numbers. Composite Numbers -  Numbers having more than two factors are called Composite numbers.

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