A number is divisible by 2 if its last digit is an even number.
Understanding Divisibility by 2
Divisibility rules are shortcuts to determine if one number can be divided by another number without leaving a remainder. The rule for 2 is one of the simplest.
The Core Rule
- If the last digit of a number is even (0, 2, 4, 6, or 8), the number is divisible by 2. This means the number can be divided by 2 with no remainder.
Examples
Let's look at some examples:
| Number | Last Digit | Divisible by 2? | Explanation |
|---|---|---|---|
| 12 | 2 | Yes | The last digit, 2, is even. |
| 15 | 5 | No | The last digit, 5, is not even. |
| 100 | 0 | Yes | The last digit, 0, is even. |
| 347 | 7 | No | The last digit, 7, is not even. |
| 1238 | 8 | Yes | The last digit, 8, is even. |
| 987654 | 4 | Yes | The last digit, 4, is even, indicating the number is divisible by 2 even if the number seems large. |
Practical Insights
- This rule is very useful for quickly checking if a number is even or odd.
- It's a fundamental concept in arithmetic and number theory.
- Knowing this rule can simplify calculations and problem-solving involving divisibility.
How it works - Deeper Explanation
- A number can be represented by multiplying its digits with their place value powers of 10. For example, 123 can be represented as 1 100 + 2 10 + 3 * 1.
- Any power of 10 (10, 100, 1000...) is divisible by 2. The only digit that would determine divisibility is the ones digit which is multiplied by 1.
- Therefore, if the ones digit is divisible by 2, the whole number will be divisible by 2.
- Since even numbers are divisible by 2, if the last digit is even (0, 2, 4, 6 or 8), then the number is divisible by 2.
In summary, determining divisibility by 2 is as simple as checking the last digit of the number.
