The document outlines various types of number systems, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It describes key mathematical concepts such as prime numbers, least common multiple (LCM), and highest common factor (HCF), with examples for clarity. Each type of number is defined alongside its notation and properties.

1. NUMBER SYSTEM!!

2. THE REAL NUMBER SYSTEM
RATIONAL NUMBERS IRRATIONAL NUMBERS
• NATURAL NUMBERS
• WHOLE NUMBERS
• INTEGERS

3.  NATURAL
NUMBER
The set of numbers from 1 to
infinite is known as natural
numbers.
NaturaL numbers are denoted by N
EX: 1 2 3 4 5 6.....

4.  WHOLE NUMBERS
The set of numbers starting from 0 to infinite is
known as whole number
Whole numbers are denoted by W
EX: 0 1 2 3 4 5 6.....

5.  INTEGERS
The integers are the numbers including whole
numbers and negative whole numbers which
can be represented on a number line and
extended upto infinity
Integers are denoted by Z
EX: -4 –3 –2 –1 0 1 2 3 4 ….

7.  REAL NUMBERS
ALL THE RATIONAL AND IRRATIONAL
NUMBERS MAKE UP THE COLLECTION
OF REAL NUMBERS
EVERY NUMBER IS REPRESENTED BY
UNIQUE REAL NUMBER.
REAL NUMBER IS DENOTED BY R

8. • RATIONAL NUMBERS
In mathematics, a rational number is
any number that can be expressed as the
quotient or fraction p/q of two integers, a
numerator p and a non-zero denominator q. Since
q may be equal to 1, every integer is a rational
number

9. • IRRATIONAL
NUMBERS
AN IRRATIONAL IS A NUMBER THAT CAN
BE EXPRESSED AS A FRACTION FOR AN
INTEGERS AND A IRRATIONAL NUMBER
HAVE DECIMAL EXPANSIONS THAT NEITHER
TERMINATE NOR BECOME PERODIC=

11. ODD NUMBER
• An odd number IS AN INTEGER
WHICH IS NOT A DIVISIBLE OF
TWO. IF IT IS DIVISBLE BY TWO
THE RESULT IS A FRACTION
EX: 1 3 5......

12. EVEN NUMBER
• AN NUMBER IS AN INTEGER WHICH IS
EVENLY DIVISIBLE BY 2
• EX: 2 4 6........

14. PRIME NUMBERS
• A PRIME NUMBER IS A WHOLE NUMBER
GREATER THAN 1, WHOSE ONLY TWO
WHOLE-NUMBER FACTORS ARE 1 AND ITSELF.
• THE FIRST FEW PRIME NUMBERS ARE 2 3 5 7
11 17 19 23 …....

16. LEAST COMMON MULTIPLE (L.C.M)
• Least common multiple (LCM) The least
common multiple (LCM) of 2 numbers is the
smallest number that they both divide evenly
into. One good way to find the least common
multiple of 2 numbers is to multiply both
numbers by 1,2,3,4,5... and then find the first
multiple that appears in both lists.

17. HIGHEST COMMON
FACTOR {H.C.F}
• HIGHEST COMMON FACTOR (H.C.F).
The Highest Common Factor (H.C.F) of two
(or more) numbers is the largest number that
divides evenly into both numbers. In other
words the H.C.F is the largest of all the
common factors. The common factors or of
12 and 18 are 1, 2, 3 and 6.

18. THANK YOU :)))
BY : SRUSHTI R SHETTY