# Number System

1. Natural Numbers: Numbers starting from 1, 2, 3 and so on so forth are
counted as Natural numbers. They are 1, 2, 3, 4….
Exceptions: Zero, negative and decimal numbers are not counted in this list.
2. Whole numbers: Zero and all other natural numbers are known as natural
numbers. They are 0, 1, 2, 3, 4….
3. Integers: They are the numbers which include all the whole numbers and
their negatives. They are …-4, -3, -2, -1, 0, 1, 2, 3, 4….
4. Rational Numbers: All the numbers which are terminating, repeating and
can be written in the form p/q, where p and q are integers and q should not be
equal to 0 are termed as rational numbers.
Example: 0.12121212….
5. Irrational Numbers: All the numbers which are non-terminating, nonrepeating and cannot be written in the form p/q, where p and q are integers
and q should not be equal to 0 are termed as irrational numbers.
Example: pie, e
6. Real Numbers: All the numbers existing on the number line are real
numbers. The group is made up of all rational and irrational numbers.
7. Imaginary Numbers: Imaginary numbers are the numbers formed by the
product of real numbers and imaginary unit ‘i’.
This imaginary unit is defined as following: i
2= -1, multiplication of this ‘i’ is calculated according to the above
value. Example: 8i
8. Complex Number: The numbers formed by the combination of real
numbers and imaginary numbers are called the complex number. Every
complex number is written in the following form:
A+iB, where A is the real part of the number and B is the imaginary part.
9. Prime numbers: All the numbers having only two divisors, 1 and the
number itself is called prime number. Hence, a prime number can be written as
the product of the number itself and 1.
Example: 2, 3, 5, 7 etc.
10. Composite Numbers: All the numbers which are not prime are called
composite numbers. This number has factors other than one and itself.
Example: 4, 10, 99, 105, 1782 etc.
11. Even & Odd Numbers: All the numbers divided by 2 are even numbers.
Whereas the ones not divisible by 2 are odd numbers.
Example: 4, 6, 64, 100, 10004 etc are all even numbers.
3, 7, 11, 91, 99, 1003 are all odd numbers.
12. Relative Prime Numbers/Co-prime Numbers: Numbers which do not
have any common factor other than 1 are called co-prime numbers.
Example: 5 and 17 are co-primes.
13. Perfect Numbers: All the numbers are called perfect numbers if the sum
of all the factors of that number, excluding the number itself and including 1,
equalizes the to the number itself then the number is termed as a perfect
number.
Example:6 is a perfect number. As the factors of 6= 2 and 3.
As per the rule of perfect numbers, sum= 2+3+1 = 6. Hence, 6 is a perfect
number.
###### Some important properties of Numbers:
• The number 1 is neither prime nor composite.
• The only number which is even is 2.
• All the prime numbers greater than 3 can be written in the form of
(6k+1) or (6k-1) where k is an integer.
• Square of every natural number can be written in the form 3n or (3n+1)
and 4n or (4n+1).
• The tens digit of every perfect square is even unless the square is ending
in 6 in which case the tens digit is odd.
• The product of n consecutive natural numbers is always divisible by n!,
where n!= 1X2X3X4X….Xn (known as factorial n). 