1. Introduction to Even Numbers
Even numbers are numbers that can be divided into two equal parts without leaving any remainder. They appear naturally in everyday life whenever things are grouped in pairs.
If a number ends with 0, 2, 4, 6, or 8, it is an even number.
2. Definition of Even Numbers
An even number is any integer that is divisible by 2.
In simple terms: If a number can be written as \(2 \times n\), where \(n\) is an integer, then it is even.
Examples:
- \(2 = 2 \times 1\)
- \(8 = 2 \times 4\)
- \(0 = 2 \times 0\)
3. Identifying Even Numbers
You can easily recognize an even number by looking at its last digit.
3.1. Last Digit Rule
If a number ends in 0, 2, 4, 6, or 8, it is even.
Examples:
- 14 → ends in 4 → even
- 102 → ends in 2 → even
- 1008 → ends in 8 → even
3.2. Using Division
If dividing a number by 2 gives a whole number, it is even.
Examples:
- \(16 \div 2 = 8\) → whole number → even
- \(7 \div 2 = 3.5\) → not whole → not even
4. Properties of Even Numbers
Even numbers follow predictable patterns in math.
4.1. Even ± Even
Even number plus or minus another even number is always even.
- \(8 + 4 = 12\)
- \(10 - 6 = 4\)
4.2. Even × Even
The product of two even numbers is always even.
- \(4 \times 6 = 24\)
- \(2 \times 10 = 20\)
4.3. Even × Odd
An even number multiplied by an odd number is always even.
- \(2 \times 3 = 6\)
- \(8 \times 5 = 40\)
4.4. Even Number Examples
Some even numbers are: -10, -2, 0, 2, 4, 6, 8, 20, 100, 256.
5. Even Numbers in Real Life
Even numbers appear in many everyday situations.
5.1. Pairs
Even numbers can form perfect pairs. For example, 6 socks can be paired into 3 pairs.
5.2. Sharing Equally
If a group of items can be divided equally between two people, the total count is even.
5.3. Time and Calendar
Many even numbers appear in timekeeping: 2 hours, 4 weeks, 6 minutes, etc.
6. Difference Between Even and Odd Numbers
Even numbers always end in 0, 2, 4, 6, 8, while odd numbers end in 1, 3, 5, 7, 9.
6.1. Comparison Table
| Even Numbers | Odd Numbers |
|---|---|
| Divisible by 2 | Not divisible by 2 |
| End with 0, 2, 4, 6, 8 | End with 1, 3, 5, 7, 9 |
| Examples: 2, 8, 14 | Examples: 3, 7, 21 |
7. Practice Questions
- Is 28 an even number?
- Is 0 an even number?
- Write the next five even numbers after 12.
- Is -6 an even number?
- Which of these are even: 17, 42, 59, 88?
8. Summary
Even numbers are integers that can be divided by 2 without a remainder. They end in 0, 2, 4, 6, or 8 and follow predictable rules in arithmetic. Even numbers help in pairing, grouping, and equal sharing in everyday life.