In mathematics, parity is the property of an integer of whether it is Even Numbers and Odd Numbers. An integer’s parity is even if it is divisible by two with no remainders left and its parity is odd if it isn’t; that is, its remainder is 1.Even Numbers and Odd Numbers have opposite parities
Any number which is divided by 2 and gives a remainder of 0 is called an even number.
Any number which is not divisible by 2 and the remainder in the case of an odd number is always “1”.
*The property by which we classify an integer in math as even or odd is also known as parity.
Identifying Even Numbers and Odd Numbers
1. By comprehending the number at “ones” place
- Here, we analyze the number at “ones” place in an integer to check if the number is even or odd.
- All the numbers ending with 1,3,5,7 and 9 are odd numbers. For example, numbers such as 11, 23, 35, 47 etc. are odd numbers.
- All the numbers ending with 0,2,4,6 and 8 are even numbers. For example, numbers such as 14, 26, 32, 40 and 88 are even numbers.
2. By grouping
- As two equal groups
If we divide a number into two groups with an equal number of elements in each, then the number is an even number. In the case of odd numbers, we get a remainder of 1 while grouping.
- As groups of “two” in each
For a number, if it forms multiple groups of “two” without any remainder, it is an even number. In the case of a remainder, a number is an odd number.
Properties of Even and Odd Numbers:
The various properties of even and odd numbers:
- The sum of two even numbers is an even number
- The sum of two odd numbers is an even number
- The sum of even and an odd number is an odd number
- Even number is divisible by 2, and leaves the remainder 0
- An odd number is not completely divisible by 2, and leaves the remainder 1.
- An even number ends with 0, 2, 4, 6, and 8
- An odd number ends with 1, 3, 5, 7, and 9