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.