# Even and odd numbers

Even and odd numbers are straightforward concepts. I will start easy, but I will try to challenge the topic a little bit

Even numbers

An even number is any number that can be divided by 2.For example, 12 can be divided by 2, so 12 is even.

We saw in divisibility rules that a number is divisible by 2 if its last digit is 0,2,4,6,or 8.

Therefore, any number whose last digit is 0, 2, 4, 6, or 8 is an even number

Other examples of even numbers are 58, 44884, 998632, 98, 48, and 10000000

Formal definition of an even number:

A number n is even if there exist a number k, such that n = 2k where k is an integer

This is formal way of saying that if n is divided by 2, we always get a quotient k with no remainder

Having no remainder means that n can in fact be divided by 2

Odd numbers

An odd number is any number that cannot be divided by 2.For example, 25 cannot be divided by 2, so 25 is odd.

We saw in divisibility rules that a number is divisible by 2 if its last digit is 0,2,4,6,or 8.

Therefore, any number whose last digit is not 0, 2, 4, 6, or 8 is an odd number

Other examples of odd numbers are 53, 881, 238637, 99, 45, and 100000023

Formal definition of an odd number:

A number n is odd if there exist a number k, such that n = 2k + 1 where k is an integer

This is formal way of saying that if n is divided by 2, we always get a quotient k with a remainder of 1

Having a remainder of 1 means that n cannot in fact be divided by 2

Basic operations with even and odd numbers

even + even = even

4 + 2 = 6

even + odd = odd

6 + 3 = 9

odd + odd = even

13 + 13 = 26

Multiplication

even × even = even

2 × 6 = 12

even × odd = even

8 × 3 = 24

odd × odd = odd

3 × 5 = 15

Subtraction

even − even = even

8 − 4 = 4

even − odd = odd

6 − 3 = 3

odd − odd = even

13 − 3 = 10

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