Even numbers are integers that can be exactly divided by 2 without leaving a remainder.

Here are the detailed properties of even numbers along with examples to illustrate them:

Properties of Even Numbers:

1. Divisibility by 2:
   • An even number is any integer that can be divided by 2 with no remainder.
   • Example: 4 ÷ 2 = 2 (no remainder), so 4 is an even number.
2. Last Digit:
   • The last digit (units place) of an even number is always 0, 2, 4, 6, or 8.
   • Examples: 10, 22, 34, 46, 58 are all even numbers.
3. Sum of Even Numbers:
   • The sum of two even numbers is always even.
   • Example: 6 + 8 = 14 (both 6 and 8 are even, and their sum 14 is also even).
4. Difference of Even Numbers:
   • The difference between two even numbers is always even.
   • Example: 10 – 4 = 6 (both 10 and 4 are even, and their difference 6 is also even).
5. Product of Even Numbers:
   • The product of an even number with any other integer is always even.
   • Example: 4 × 3 = 12 (4 is even, and the product 12 is also even).
6. Quotient of Even Numbers:
   • The quotient of two even numbers may be even or odd, but if it results in an integer, the result will also be an integer.
   • Example: 8 ÷ 2 = 4 (both 8 and 2 are even, and the quotient 4 is even).

Examples:

• Example 1: 2, 4, 6, 8, 10 are all even numbers.
• Example 2: 14 + 20 = 34 (both 14 and 20 are even, and their sum 34 is also even).
• Example 3: 18 – 10 = 8 (both 18 and 10 are even, and their difference 8 is also even).
• Example 4: 4 × 5 = 20 (4 is even, and the product 20 is also even).
• Example 5: 12 ÷ 6 = 2 (both 12 and 6 are even, and the quotient 2 is even).

Visual Representation:

Here are some examples to help illustrate these properties:

1. Divisibility by 2: Example: 4 ÷ 2 = 2
2. Sum of Even Numbers: Example: 6 + 8 = 14
3. Difference of Even Numbers: Example: 10 – 4 = 6
4. Product of Even Numbers: Example: 4 × 3 = 12
5. Last Digit of Even Numbers: Examples: 10, 22, 34, 46, 58

These examples help to understand the properties of even numbers.