A number that can be divided by 2 is an even number. An easy way to check whether a number is even or odd is to check whether 2 can divide the last digit of number. If the last digit can be divided by 2 then the number is even else the number is odd.
As an even number will always be divisible by 2 hence any even number can be written as -> 2k (where k is an integer)
As an odd number will never be divisible by 2 hence any odd number can be written as -> 2k + 1 (where k is an integer)
For e.g.
1) Find 234 is odd or even.
The last digit of 234 is 4. 4 is divisible by 2. Hence 234 is an even number.
2) Find 843 is odd or even.
The last digit of 843 is 3. 3 is not divisible by 2. Hence 843 is odd.
EFFECT OF OPERATION ON ODD AND EVEN NUMBER->
- ADDITION OR SUBTRACTION ->
- When 2 EVEN numbers are added the resulted number will also be EVEN.
EVEN + EVEN = EVEN
Let’s find why this happens,
EVEN number can be written in the form 2n
EVEN + EVEN = 2n + 2m
=2(n + m)
As 2(n + m) will always be divisible by 2 hence it is an even number.
EVEN + EVEN = EVEN
- When 2 ODD numbers are added the resulted number will be EVEN.
ODD + ODD = EVEN
Let’s find why this happens,
ODD number can be written in the form (2n + 1)
EVEN + EVEN = (2n + 1) + (2m + 1)
= 2n + 2m + 2
=2(n + m + 1)
As 2(n + m + 1) will always be divisible by 2 hence it is an even number.
ODD + ODD = EVEN
- When 1 ODD numbers and 1 even number are added together the resulted number will be ODD.
ODD + EVEN = ODD
Let’s find why this happens,
ODD number can be written in the form (2n + 1)
EVEN number can be written in the form (2m)
ODD + EVEN = (2n + 1) + (2m)
= 2n + 2m + 1
=2(n + m) + 1
As (2(n + m) + 1) will never be divisible by 2 hence it is an odd number.
ODD + EVEN = ODD
1^{st} NUMBER |
2^{nd} NUMBER |
ADDITION OF 1^{ST} AND 2^{ND} NUMBER |
EVEN |
EVEN |
EVEN |
ODD |
ODD |
EVEN |
EVEN |
ODD |
ODD |
ODD |
EVEN |
ODD |
- MULTIPLICATION ->
If any of the number we are multiplying has even number in it the resulted number will always be even.
ODD * EVEN = EVEN
Let’s find why this happens,
ODD number can be written in the form (2n + 1)
EVEN number can be written in the form (2m)
ODD * EVEN = (2n + 1) * (2m)
=2(m)(2n + 1)
As (2(m)(2n + 1)) will always be divisible by 2 hence it is an even number.
1^{st} NUMBER |
2^{nd} NUMBER |
MULTIPLICATION OF 1^{ST} AND 2^{ND} NUMBER |
EVEN |
EVEN |
EVEN |
EVEN |
ODD |
EVEN |
ODD |
EVEN |
EVEN |
ODD |
ODD |
ODD |