CLASS-8
CLASSIFICATION OF NUMBER

CLASSIFICATION OF NUMBERS

Even Numbers –

Numbers which not leave any reminders on being divided by 2 is called EVEN numbers. In other words, the number that multiple of 2 is called EVEN numbers.

For example-  0, 2, 4, 6, 8, 12, 14, 16,……. 96,……. 256,…. 1024,…… 2048,…….. 4096 are even numbers.

The even digit are 0, 2, 4, 6, & 8 any number having an even digit in the units place is an even number.

Odd Numbers –

Numbers that are not exactly divisible by 2 is called ODD numbers. In other words, a number that are not multiples of 2 is called ODD numbers.

For example – 1, 3, 5, 7, 9,………37, 39,…….., 125,…… 4137,………. 18249 are ODD numbers

The Odd digits are 1, 3, 5, 7, & 9 any number having an odd digit in the units place is an odd numbers.

Prime Numbers –

A number would be called a PRIME number if it has no other factors except 1 and itself. For example – 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 51,…….. are some PRIME numbers. 2 is only Even Prime number and it is the smallest prime numbers.

Composite Number –

A number which has two or more Prime factors is called a COMPOSITE numbers. 4, 6, 8,……, 21,……136 are some composite numbers.

Co-Prime Numbers –

Two numbers are called COPRIME or RELATIVELY PRIME numbers, if they do not have common factors except 1. For example – 3 & 4, 17 & 21, 23 & 25 are co-prime numbers.

Twin-Prime –

Pairs of Prime Numbers that, differ by 2 is called TWIN PRIME . for example – 3 & 5, 5 & 7, 11 & 13, 17 & 19 is some examples of twin primes.

Prime Factorization –

Writing a number as a product of Prime numbers is called PRIME FACTORIZATION

For example – a)  96 =  2 X 2 X 2 X 2 X 2 X 3

                b) 12500 = 2 X 2 X 5 X 5 X 5 X 5 X 5

Method of Prime Factorization –

Divide the number repeatedly by prime numbers 2, 3, 5, 7,……….. till the quotient is 1. Alternatively break the number into smaller factors till all the factors are prime.

Example.) Express 2500 as a product of Prime –

Answer.)   2500   =    2 X 1250 

                     =   2 X 2 X 625

                     =   2 X 2 X 5 X 125

                     =   2 X 2 X 5 X 5 X 25

                     =   2 X 2 X 5 X 5 X 5 X 5

Another method –

So,  2500 = 2 X 2 X 5 X 5 X 5 X 5