Wednesday 17 October 2012
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.
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.
