Even And Odd Numbers

Even and Odd Numbers Definition:

Normally the even and odd numbers definition is, “Even numbers are those numbers which are divisible by 2 and odd numbers which are not divisible by two”.

OR, in simple language,

“Even numbers are those which when divided by 2 leaves no remainder or as 0 and Odd numbers are those numbers which when divided by 2 leaves a remainder of 1”.

The sets of even and odd numbers can be expressed as follows,

  • Even = { 2k : k \(\epsilon\) Z }
  • Odd = { 2k + 1 : k \(\epsilon\)  Z }

A formal definition of an even number is an integer of the form n = 2k, where k is an integer. An odd number is defined as an integer of the form n = 2k + 1. This classification applies only to integers. Non integer numbers like 1/2, 4.201, or infinity are neither even nor odd.

For easy understanding, we can say that Even is when it can be divided equally in two and odd is when while dividing for two 1 is left over. This means that in even we can distribute equally between two people or group but in odd we cannot divide equally.

Flow-chart for Even and Odd Numbers Explanation:

Even And Odd Numbers

Even and odd numbers examples:

Even numbers Odd numbers
2 1
4 3
6 5
8 7

To check that whether a number is even or odd:

As we know now that “Even numbers those numbers which ends with 0,2,4,6,8 and odd numbers are those numbers which end with 1,3,5,7,9.”

So, First look at the number in the one’s place. This single number will tell whether the entire number is odd or even. An even number ends in 0, 2, 4, 6, or 8. An odd number ends in 1, 3, 5, 7, or 9.

Why zero is an even number?

Zero is an even number because it is an integer multiple of 2, specifically 0 × 2.

Even and Odd Decimals:

Decimals are not even or odd numbers because they are not whole numbers. For example, you can’t say that the fraction 1/3 is odd by the fact that a denominator is an odd number or 12.34 as an even as its last digit is even. Only integers can be even, or odd, meaning decimals and fractions cannot be even or odd. Zero, however, is an integer and is divisible by two, so it is even. Odd numbers are those numbers not evenly divisible by two.

Stay tuned with BYJU’S to learn more about numbers, prime number and many more.

Practise This Question

The cost price of a pen is ₹ 12. But the shopkeeper sold it for ₹ 18. What is the percentage of profit obtained by the shopkeeper?