even numbers, odd numbers

Positive whole numbers and negative whole numbers, in math called Integers, can be included in two categories. They are:

• Even numbers
• Odd numbers

The property of an integer's inclusion in one of two categories: even or odd, in mathematics is called parity.

Even numbers

Even numbers are integers and when they are divided by two, the result is an integer or leaves no remainder.

Examples of even numbers are 2, 6, 18, 30, and 454.

So, if we have 8 apples, and we divide them into two equal groups, the result is 4 apples in both groups. There will be no apple on the side. As a result, we have an integer, and as we can see, there is no remainder.

Regardless of how many digits the number has, all Even numbers end with a digit 0, 2, 4, 6, or 8. 

• The number 36 is an even number because it ends in 6.
• The number 458 is an even number because it ends in 8.
• The number 78642 is an even number because it ends in 2.

Even numbers can be negative numbers too. Examples of negative even numbers are -198, -116, -92, -40, -16, etc.

Zero is considered an even number.

Odd numbers

Odd numbers are integers and when they are divided by 2, the result is a non-integer or leaves a remainder of 1. Their position is between the even numbers.

Examples of odd numbers are 1, 7, 13, 29, 59, 111, 245, etc.

If we have 7 apples, and we divide them into two equal groups, the result is 3 apples in both groups, but there is 1 apple left. As a result, we have a non-integer, or we have a remainder 1.

Odd numbers end in digits: 1, 3, 5, 7, and 9, regardless of how many digits the number has. 

• 75 is an odd number because it ends in 5
• 133 is an odd number because it ends in 3
• 34677 is an odd number because it ends in 7

Since odd numbers are integers, they can be negative numbers too. Examples of negative odd numbers are -215, -135, -111, -87, -53, -29, -7, etc.
 

Adding, subtracting, and multiplying even and odd numbers
 

1. Adding even and odd numbers

Operation	Result	Example
Even+ Even	Even	\(4+16=20\)
Even + Odd	Odd	\(18+9=27\)
Odd + Even	Odd	\(23+12=35\)
Odd + Odd	Even	\(7+25=32\)

 

2. Subtracting even and odd numbers

Operation	Result	Example
Even − Even	Even	\(36-14=22\)
Even − Odd	Odd	\(16-1=15\)
Odd − Even	Odd	\(45-14=31\)
Odd − Odd	Even	\(23-3=20\)

3. Multiplying even and odd numbers

Operation	Result	Example
Even × Even	Even	\(2\times6=12\)
Even × Odd	Even	\(8\times7=56\)
Odd × Even	Even	\(5 \times 6=30\)
Odd × Odd	Odd	\(3 \times 3=9\)