Number System covers various types of numbers viz. natural numbers, whole numbers, integers, rational and irrational numbers which constitutes the Real number system.
VARIOUS TYPES OF NUMBERS
1. Natural Numbers: All the positive numbers 1, 2, 3 ,.., etc. that are used in counting are called Natural numbers. Types of Natural Numbers based on divisibility:
Examples for Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, etc.
Note: Unity, i.e. 1 is not prime number.
Examples for composite numbers are 4, 6, 8, 9, 10, 14, 15, etc.
2. Whole Numbers: All counting numbers and 0, form the set of whole numbers.
For example: 0, 1, 2, 3…, etc. are whole numbers.
3. Integers: All counting numbers, Zero and negative of counting numbers, form the set of integers.
Therefore,…-3, -2, -1, 0, 1, 2, 3,.. are all integers.
4. Rational Numbers
A number which can be expressed in the form p/q, where p and q are integers and q≠0, is called a rational number.
For example 2 can be written as 2/1, therefore 2 is also a rational number.
5. Irrational Numbers
Numbers which are not rational but can be represented by points on the number line called irrational numbers.
6. Even and Odd Numbers
Numbers divisible by 2 are called even numbers whereas numbers that are not divisible by 2 are called odd numbers.
For example 2, 4, 6, etc are even numbers and 3, 5, 7, etc are odd numbers.
The following rules related to Even and Odd numbers are important:
Factors and Co-Primes
Factorization Method for LCM and HCF
For example: 15 = 3 X 5
18 = 32 X 2
24 = 23 X 3
Now take all primes number the given numbers and write their maximum powers. So LCM of 15, 18, 24 =23 X 32 X 5 = 360
18 = 32 X 2
Now, HCF of 12 and 18 = 3 X 2 = 6
TESTS OF DIVISIBILITY OF NUMBERS
LAWS OF INDICES
Middle Term of Binomial Theorem:
We hope that these concepts along with their associated practice test would help you in your preparation of Number System chapter.
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