A number is divisible by 8 if its last three digits form a number that is divisible by 8. This works because 1000 is divisible by 8 (1000 = 8 * 125), and any larger number can be expressed as a multiple of 1000 plus its last three digits.
Understanding the Divisibility Rule of 8
The divisibility rule for 8 hinges on the fact that 1000 is a multiple of 8. Therefore, whether a number is divisible by 8 depends entirely on the last three digits.
- Method: Examine only the last three digits of the number.
- Test: Determine if this three-digit number is divisible by 8. You can do this through simple division.
- Result: If the three-digit number is divisible by 8 (with no remainder), then the original, larger number is also divisible by 8.
Examples
- Is 12856 divisible by 8? The last three digits are 856. 856 / 8 = 107. Since there's no remainder, 12856 is divisible by 8.
- Is 3472 divisible by 8? The last three digits are 72. 72 / 8 = 9. This means 3472 is divisible by 8.
- Is 987654321 divisible by 8? The last three digits are 321. 321 / 8 = 40.125. Since there is a remainder, 987654321 is not divisible by 8.
Practical Insights
This rule is particularly useful for large numbers where direct division by 8 might be time-consuming. By focusing on the last three digits, you significantly simplify the divisibility check. Many calculators and programming languages handle large numbers efficiently but this rule provides a mental shortcut.
