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.

     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.

Factorisation - The process of finding two or more expressions whose product is the given expression is called factorisarion. 

Rational numbers :- The numbers of the form p/q , where p and q are integers and q is not equal to zero, q≠ 0 , are called rational numbers.  0 is neither positive nor negative.  Example-  Numbers 3/5 , -1/14 is a rational number.  - Every integer is a rational number.  - Every whole number is a rational number because every whole number can be expressed as a fraction. Positive rationals - A rational number is said to be positive if its numerator and denominator are either both positive or both negative.  Example - 3/7 or -6/11 are positive rationals.  Negative rationals - A rational number is said to be negative if its numerator and denominator are of opposite signs.  Example- -7/9, 4/-11 are negative rationals.  Some important facts :- 1. The product of a rational number and its reciprocal is 1. 2.  Zero '0' has no reciprocal.  3. The reciprocal of a positive rational number is positive.  4. The reciprocal of a negative rational number is negative.  5. Every natural number N