Various Types of Numbers

Even Numbers

Any whole number which is exactly divisible by 2 is called an even number.

Example: 2, 4, 6, 8, 10 ……..etc. are even numbers.

OR

Any number in which digit at ones place is 0, 2, 4, 6, or 8 is an even number.

Example: 148, 222, 436, 120, 444 are even numbers.

OR

Even number is a number that can be divided into pairs of 2

Odd Numbers

Any whole number which cannot be exactly divisible by 2 is called an odd number.

Example: 1, 3, 5, 7, 9 ……..etc. are odd numbers.

OR

Any number in which digit at ones place is 1, 3, 5, 7, or 9 is an odd number.

Example: 141, 223, 435, 127, 449 are odd numbers.

OR

Odd number is a number that cannot be divided into pairs of 2

Prime Numbers

Number which has only two factors i.e. 1 and the number itself is called prime number.

Example: 2, 3, 5, 7, 11, 13, 17, 19, 23 etc. are prime numbers.

Twin Prime Numbers

Two prime numbers whose difference is 2 are called twin prime numbers.

Example: 3 and 5, 17 and 19

Co-prime Numbers

Any two numbers are considered as co-prime, if they do not have common factor other than 1. Co-prime number need not be necessarily prime numbers.

Example: 4 and 5

Composite Numbers

Number which has more than two factors is called composite number.

Example: 4, 6, 8, 9, 10, 12 etc. are composite numbers.

Prime Factorization Method

It is a method of finding all the prime numbers which multiply to make the given number.

Method 1: Factor Tree Method

Example: 

32 = 2 x 2 x 2 x 2 x 2

Explanation:

8 x 4 = 32, write factor 8 and 4 below 32

2 x 4 = 8, write factor 2 and 4 below 8

2 x 2 = 4, write factor 2 and 2 below 2

2 x 2 = 4, write factor 2 and 2 below 2

Now, we cannot factor further, so prime factor are the last number at each node.

Method 2: Prime Factorization Method

Example:

32 = 2 x 2 x 2 x 2 x 2

Explanation:

Start dividing 32 by the smallest prime number i.e. 2

32 ÷ 2 = 16

16 is composite number, so divide 16 again by 2

16 ÷ 2 = 8

8 is composite number, so divide 8 again by 2

8 ÷ 2 = 4

4 is composite number, so divide 4 again by 2

4 ÷ 2 = 2

2 is prime number

Point to be remembered

      1.   Composite number can be written as a product of its prime factors.

      Example: 24 = 2 x 2 x 2 x 3

      2.   No two numbers can have the same prime factors.

      Example: 24 = 2 x 2 x 2 x 3 and 32 = 2 x 2 x 2 x 2 x 2

      3.   1 is neither a prime number nor a composite number.