Types Of Numbers

Types of Numbers

Even Numbers:

In the given number the number in its units place is either 0, 2, 4, 6 or 8, and then the number is an even number.

(Or)

If the given number is divisible by 2 then the number is also an even number.

Odd Numbers:

In the given number the number in its units place is either 1, 3, 5, 7, or 9, and then the number is an odd number.

(Or)

If the given number leaves remainder 1 when divided by 2 then the number is also an odd number.

Prime Numbers:

If the given numbers are having the factors 1 and the number itself then the numbers are called prime numbers.

Examples: 2= 1x2, 3=1x3, 5= 1x5, 7= 1x7, 11=1x11, 13=1x13 …etc

The prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37 …etc

Note:  2 is the only even prime number.

Twin Primes:

If two prime are differed by 2 then they are twin primes.

Examples: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43) …etc

Co Primes:

If the HCF or GCD of 2 numbers is 1 then the numbers are said to be co primes.

Example:  (3, 4), (4, 5),(5, 18),(9, 20) …etc

Composite Number:

If a number is having more than 2 factors then they are called composite numbers.

Examples: 4, 6, 8, 9, 10, 12, 14, 15 … etc

Factors of 4 = 1, 2, 4.

Factors of 6 = 1, 2, 3, 6.

Factors of 8 = 1, 2, 4, 8.

Note:

1. 4 is the smallest composite number.

2. 1 is neither prime nor composite number.

Perfect Number:

If the sum of the factors of the given number is twice the given number then the number is said to be a perfect number.

Example:

1.       6 is a perfect number.

The factors of 6 are 1, 2, 3, 6.

Sum of the factors = 1+2+3+6

                            =12

                                     = 2x6

Number System

Natural Numbers (N):

                The numbers starts from 1, 2, 3 ... etc; are called Natural numbers. Natural numbers are denoted by ‘N’.

N= {1, 2, 3 …}

Whole Numbers (W):

The numbers starts from 0, 1, 2, 3 ... etc; are called Whole numbers. Whole numbers are denoted by ‘W’.

W= {0, 1, 2, 3 …}

Integers (I or Z):

The numbers etc…, -3,-2,-1, 0, 1, 2, 3 … etc; are called Integers. Integers are denoted by I or Z.

Z= {…, -3,-2,-1, 0, 1, 2, 3 …}

Rational Numbers (Q):

The numbers which can be written in the form of p/q, q≠0, where p and q are integers are called Rational numbers. Rational numbers are denoted by ‘Q’.

Examples: ⅓, ⅔,-⅕, ⅖,-⅘, ⅜,-⅞, 0,-1,-2,-3,-4, 1, 2, 3, 4 … etc

Note:

1. Zero {0} is also a rational number.

2. All rational numbers are not fractions but all fractions are rational numbers.

Irrational Numbers {Q’}:

The numbers which cannot be written in the form of p/q, q≠0, where p and q are integers are called Irrational numbers. Irrational numbers are denoted by ‘Q’’.

Examples: √2, √3, √5, √6, √7, etc.

Real Numbers {R}:

It is the combination of all of the above numbers i.e. N, W, Z, Q and Q’. Real numbers are denoted by ‘R’.