Types of Numbers???

Types of Numbers???

Dear Aspirants;

The following are the types of numbers :-

1.Natural Numbers : Counting numbers 1, 2, 3, 4, 5,..... are called natural

numbers.

2.Whole Numbers : All counting numbers together with zero form the set of whole numbers. Thus,

(i) 0 is the only whole number which is not a natural number.

(ii) Every natural number is a whole number.

3.Integers  :  All  natural  numbers,  0  and  negatives  of  counting  numbers  i.e.,

{…, - 3 , - 2 , - 1 , 0, 1, 2, 3,…..} together form the set of integers.

(i) Positive Integers : {1, 2, 3, 4, …..} is the set of all positive integers.

(ii) Negative Integers : {- 1, - 2, - 3,…..} is the set of all negative integers. (iii) Non-Positive and Non-Negative Integers : 0 is neither positive nor negative. So, {0, 1, 2, 3,….} represents the set of non-negative integers, while

{0, - 1 , - 2 , - 3 , …..} represents the set of non-positive integers.

4.  Even Numbers : A number divisible by 2 is called an even number, e.g., 2, 4, 6, 8,

10, etc.

5.  Odd Numbers : A number not divisible by 2 is called an odd number. e.g., 1, 3, 5, 7,

9, 11, etc.

6.  Prime Numbers : A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself.

Prime numbers upto 100 are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,

47,  53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Prime numbers Greater than 100 : Letp be a given number greater than 100. To find out whether it is prime or not, we use the following method :

Find a whole number nearly greater than the square root of p. Let k > *jp. Test whether p is divisible by any prime number less than k. If yes, then p is not prime. Otherwise, p is prime.

e.g,,We have to find whether 191 is a prime number or not. Now, 14 > V191. Prime numbers less than 14 are 2, 3, 5, 7, 11, 13.

191 is not divisible by any of them. So, 191 is a prime number.

7.Composite Numbers : Numbers greater than 1 which are not prime, are known as composite numbers, e.g., 4, 6, 8, 9, 10, 12.

Note :    (i) 1 is neither prime nor composite.

(ii) 2 is the only even number which is prime.

(iii) There are 25 prime numbers between 1 and 100.

8.  Co-primes : Two numbers a and b are said to be co-primes, if their H.C.F. is 1. e.g., (2, 3), (4, 5), (7, 9), (8, 11), etc. are co-primes,

Tags : -what is natural number, what is whole number, what is integers, what is positive integers, what is negative integers, what is even numbers, what is odd numbers, what is prime numbers, what is composite numbers, what is coprimes, what is co-primes.