Even And Odd Numbers
Natural numbers : The counting numbers are known as natural numbers.
Ex : 1, 2, 3, 4, 5 ..............
Whole numbers : The natural numbers together with ‘0’ are known as whole numbers.
Ex : 0, 1, 2, 3 .......
Even numbers : The numbers when divided by 2 give the remainder as ‘0’ are known as even numbers.
Ex : 2, 4, 6 .......
‘0’ is also an even number
Odd numbers : The numbers when divided by 2 given the remainder as ‘1’ are known as odd numbers.
Ex : 1, 3, 5, .......
Sum of first ‘n’ odd natural numbers is \(n^2\)
Sum of first ‘n’ even natural numbers is n (n+1)
Even Numbers :
1. Numbers that can be expressed in the form of 2n, where ‘n’ is a whole number.
2. Numbers that can be divided into two equal parts.
3. When we divide an even number by 2, we get the remainder 0.
4. Examples: 2, 4, 18, 26,…
5. All numbers ending with 0, 2, 4, 6, 8 are referred to as even numbers
6. The sum of two even numbers is always even
7. The product of two even numbers is always even.
Odd Numbers :
1. Numbers that can be expressed in the form of 2n + 1, where ‘n’ is a whole number.
2. Numbers that cannot be divided into two equal parts.
3. When we divide an odd number by 2, we get the remainder 1.
4. Examples: 1, 5, 7, 9, 23,…
5. All numbers ending with 1, 3, 5, 7, 9 are referred to as odd numbers.
6. The sum of two odd numbers is always even
7. The product of two odd numbers is always odd
The successor of a is a + 1.
The predecessor of a is a - 1.