EVEN AND ODD NUMBERS

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 ->
  1. 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

 

  1. 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

  1. 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

1st NUMBER
2nd NUMBER
ADDITION OF 1ST AND 2ND 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.

 

1st NUMBER
2nd NUMBER
MULTIPLICATION OF 1ST AND 2ND NUMBER
EVEN
EVEN
EVEN
EVEN
ODD
EVEN
ODD
EVEN
EVEN
ODD
ODD
ODD

 

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