Table of Contents

Last modified on August 3rd, 2023

Integers that are exactly divisible by 2 and form a remainder of 0 are called even numbers. They are multiples of 2. Some examples of even numbers are 2, 4, 6, 8, 10, and so on

Even numbers can be positive (greater than 0) or negative (smaller than 0). They can be easily represented on a number line:

3 ways of identifying an even number are:

**1. By Checking the Form of the Number**

An even number (n) is of the form 2k, such that n = 2k, where k is an integer. For example, in the even number 16, k is 8, which is another positive number.

**2. By Checking the Number in the Unit Place**

If a number is even, the digit at the one’s place is also even. For example, 34, 52, 104, and 206 are all even numbers as their ones digit are all even.

**3. By Grouping**

Suppose we divide the total number of people into 2 groups with an equal number of elements. Here, the total is an even number. For example, if we are grouping a set of 12 people into groups of 2. There will be 6 such groups without any people left. Thus, 12 is an even number.

The list of all the even numbers up to 100 is given below in the chart:

The chart below lists all the odd and even numbers from 1 to 100.

Even numbers are thus the opposite of odd numbers that are not divisible by 2.

The 3 main properties are:

- The summation of 2 even numbers is an even number (Even + Even = Even). For example, 2 + 8 = 10
- The summation of an even and an odd number gives an odd number (Even + Odd = Odd). For example, 3 + 8 = 11
- The summation of 2 odd numbers is an even number (Odd + Odd = Even). For example, 9 + 5 = 14

- The difference between 2 even numbers is an even number (Even – Even = Even). For example, 12 – 4 = 8
- The difference between an even and an odd number always gives an odd number (Even – Odd = Odd). For example, 14 – 9 = 5
- The difference between 2 odd numbers is an even number (Odd – Odd = Even). For example, 15 – 7 = 8

- The product of 2 even numbers is an even number (Even × Even = Even). For example, 6 × 8 = 48
- The product of 2 odd numbers is an odd number (Odd × Odd = Odd). For example, 5 × 3 = 15
- The product of an even and an odd number always gives an even number (Even × Odd = Even). For example, 6 × 5 = 30

Consecutive even numbers are even numbers that follow each other in a sequence, such as 2, 4, 6, 8, 10, 12, 14, and so on. They are arranged from smallest to largest.

As we know, natural numbers are counting numbers starting from 1. Thus, even natural numbers are all natural numbers that are only even, such as 2, 4, 6, 8, and so on.

**Write 4 consecutive even numbers between 15 to 25.**

Solution:

4 consecutive even numbers between 15 to 19 are {16, 18, 20, and 22}.

**Is 12846 an even number?**

Solution:

The ones place of the number 12846 is 6, which is an even number. Thus, the number 12846 is an even number.

**List out the numbers that are even in the given series:****44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55**

Solution:

The even numbers in the given series are {44, 46, 48, 50, 52, 54}

**The sum of 3 consecutive even numbers is 270. Find the numbers.**

Solution:

Let the numbers be n, n + 2, and n + 4.

∴ n + (n + 2) + (n + 4) = 270

3n + 6 = 270

3n = 264

n = 88

Thus the other numbers are

n + 2 = 88 + 2 = 90

n + 4 = 88 + 4 = 92

Thus the numbers are 88, 90, and 92

Ans. Yes, zero can be written in the form n = 2k as 0 = 2 × 0.

Last modified on August 3rd, 2023