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This course has important notes along with solved questions based on the topic of height and distance. buy practicing this course, students can easily solve any question related to the topic of height and distance.

Number System is an important topic of Quantitative Aptitude section for various competitive exams like SSC and Banking. there are questions asked on the topic of Number System. student can only solve these questions if they know shortcut trick and tips to solve these questions fastly. this course contains Important notes, short tricks & tips and Important formulas to be kept in mind. which will help students to these type of questions.

__Natural Numbers__ : Numbers which are used for counting the objects are called natural numbers. They are denoted by N.

N = { 1, 2, 3………………..}

All positive integers are natural numbers.

__Whole numbers :-__ When ‘zero’ is included in the natural numbers, they are known as whole numbers.

They are denoted by W.

W= { 0, 1, 2, 3……………….}

__Integers :__ All natural numbers, zero and negatives of natural numbers are called as integers.

They are denoted by I.

I = { ………………..,-3, -2, -1, 0, 1 , 2, 3………………}

__Rational numbers__ : The numbers which can be expressed in the form of where P and Q are integers and are called rational numbers

They are called by Q.

__Irrational numbers__ : The numbers which cannot be written in the form of where P and Q are integers and are called irrational numbers.

When these numbers are expressed in decimal form, they are neither terminating nor repeating.

__Real numbers__ : Real numbers include both rational as well as irrational numbers.

Positive or negative, large or small, whole numbers or decimal numbers are all real numbers.

e.g.= 1, 13.79, -0.01, etc.

__Imaginary numbers__ : An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit ‘i’ which is defined by its properly

Note : Zero (0) is considered to be both real and imaginary number.

__Prime number__ : A prime number is a natural number greater than 1 and is divisible only by 1 and itself.

e.g.2, 3, 5, 7, 11, 13, 17 ,19 ………….etc.

Note :- 2 is the only even prime number.

__Composite Numbers__ : A number, other than 1, which is not a prime number is called a composite number .

E.g. 4, 6, 8, 9, 10, 12, 14, 15 ……….etc.

Note :1 1 is neither a prime number nor a composite number.

2 there are 25 prime numbers between 1 and 100.

__To find whether a number is prime or not-__

To check whether the number is prime or not,

1 We take an integer larger than the square root of the number. Let the number be ‘k’.

2 Test the divisibility of the given number by every prime number less than ‘k’.

3 If it is not divisible by any of them, then the given number is prime otherwise it is a composite number.

E.g.= Is 881 a prime number ?

Sol- The appropriate square root of 881 is 30.

Prime number less than 30 are 2, 3, 5, 7, 11, 13, 17,19, 23,29.

881 is not divisible by any of the above numbers, so it is a prime minister.

__Co-prime numbers__ : Two numbers are co-prime of their HCF is 1.

E.g. (2,3), (3,4) , (5,7), (3,13) etc.

Even numbers : The number which is divisible by 2 is called even number.

E.g. – 2, 4, 6, 8…………….

__Odd numbers__ – The number which is not divisible by 2 is called odd number.

e.g.= 3, 5, 7, 9…………..

__Consecutive numbers :__ A series of numbers in which the succeeding number is greater then the preceding number by 1 is called a series of consecutive numbers.

i.e., Difference between two consecutive numbers is 1.

__Some Rules on Counting Numbers__

1. Sum of all the first n natural numbers

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