In our everyday life we see and use different kind of number. Some of they are positive, some are negative, some of them are fraction and so on.
The group of numbers which start from 1 is known as Natural Numbers. It can also be defined as those numbers which we used in our daily life for counting are known as Natural Numbers. Examples of Natural Numbers are 1, 2, 3, 4, 5, 6,34, 69, 1001 and so on.Group of Natural Numbers are denoted by ‘N’. The smallest Natural Number is 1.
Properties of Natural Numbers:
- Sum of two or more Natural Numbers is always a Natural Number. For example 2 + 3 is 5. Here 2, 3 and 5 all are Natural numbers.
- Subtraction of two Natural Numbers may be or may not be a Natural Number.For example 5 – 3 is 2 but 3 – 5 is – 2. Here 2 is a Natural number but – 2 is not a Natural number.
- Multiplication of two or more Natural Numbers is always a Natural Number.For example 3 x 2 is 6. Here 2, 3 and 6 all are Natural numbers.
- Division of two Natural Numbers may or may not be a Natural Number.
- Negative Numbers and 0 are not Natural Numbers.
- 1 is the smallest Natural Number.
The group of those numbers which start from 0 is known as whole Numbers. A group of Whole Numbers is denoted by ‘W’. The smallest Whole Number is 0.Examples of Whole Numbers are 0, 1, 4, 8, 17, 110, 15447 and so on.
Properties of Whole Numbers:
- Addition of two or more Whole Numbers is a Whole Number.
- Subtraction of two Whole Numbers may or may not be a Whole Number.
- Multiplication of two or more Whole Numbers is a Whole Number.
- Division of two Whole Numbers may or may not be a Whole Number.
- Negative numbers are not Whole Numbers.
- All Natural Numbers are Whole Numbers.
- 0 is the smallest Whole Number.
A group of numbers that contains positive and negative numbers along with 0 is known as Integers. Integers area denoted by ‘Z’. Examples of Integers are -4, -6, 0, 1, 300 and so on. An Integer can be divided into two sub categories.
- Positive Integers
- Negative Integers
Integers greater than 0 are called positive Integers. Group of Positive Integers are denoted by Z+. All Natural Numbers are positive Integers. 1, 2, 5, 9, 100 and 2648 are examples of positive Integers .
Integers less than 0 are called negative Integers. Group of Negative Integers are denoted by Z–. -1, -6, – 1001, – 5551 and – 19737 are examples of negative Integers.
Properties of Integers:
- Addition of two or more Integers is always an Integer.
- Subtraction of two Integers is always an Integer.
- Multiplication of two or more Integers is always an Integer.
- Division of two Integers may or may not be an Integer.
- All Natural numbers and Whole numbers are Integers.
- – 1 is the largest Negative Integer.
- 1 is the smallest Positive Integer.
Those numbers that can be represented by p/q where p and q are Integers and q is not equal to 0 are called Rational numbers. Examples of Rational numbers are 2/3, -6/7 and 1/5.
Properties of Rational Numbers:
- Addition, Subtraction, Multiplication and Division of Rational numbers is a Rational number.
- 0 is a Rational number because it can be represented as 0/1.
- All Natural numbers, Whole numbers and Integers are Rational numbers.
- Each Integer is a Rational Number but each Rational Number is not an Integer.
Equivalent Rational Numbers:
Rational Numbers who have same simplest value are called Equivalent Rational Numbers. For example 4/6, 6/9 and 8/12 are Equivalent Rational Numbers. Because the simplest value of each rational number is 2/3.
All those numbers which can not be represented in the form of p/q where p and q are Integers and q is not equal to 0 are known as Irrational Numbers. All square root and cube root number are irrational numbers.
Those numbers which are not divisible by 2 are called Odd numbers. 1, 3, 5, 7, 9, 11 all are examples of Odd numbers. Those numbers having any one of the digits 1, 2, 3, 5, 7 and 9 at units place are called Odd numbers. For example 123 is an odd number because it has 3 at units place.
Those numbers which are divisible by 2 are called Even numbers. 2, 4 , 6, 8, 10 and 12 are Even numbers. Numbers ending with 0, 2, 4, 6 and 8 are also termed as Even numbers.
A number which is divisible by 1 and itself is called Prime number. First 10 Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. 0 and 1 are not prime numbers.
All those numbers which are not prime numbers are called composite numbers. Composite numbers are also known as non prime numbers. 4, 6, 8, 9, 10, 12, 14, 15, 50, 100, 122 are composite numbers.
Two numbers are said to be coprime numbers if they are not divisible by any number other than 1. Example of coprime numbers are 3 and 4, 5 and 11, 11 and 13 etc. 4 and 10 are not coprime because they are divisible by 2 other than 1. There is an alternative definition for coprime numbers and it as if The HCF of two numbers is 1 then they are coprime numbers.
Twin Prime Numbers:
A pair of prime numbers having difference of two are called twin prime numbers. For example 3 and 5 are twin prime number because difference of 3 and 5 is 2. But 7 and 11 are not twin primes because difference of 7 and 11 is 4. Other twin primes are as 5 and 7, 11 and 13, 17 and 19, 29 and 31, 41 and 43 and so on.