A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
Understanding the Divisibility Rule of 8
The divisibility rule for 8 is a simple shortcut to determine if a larger number is evenly divisible by 8 without performing long division. Instead of dividing the entire number, you only need to examine the last three digits.
How it Works:
- Identify the last three digits: Take the last three digits of the number you want to check.
- Check for divisibility by 8: Determine if this three-digit number is divisible by 8. You can do this through division or by recognizing multiples of 8.
- Conclusion: If the three-digit number is divisible by 8, then the original larger number is also divisible by 8. If not, the original number is not divisible by 8.
Examples:
- 123456: The last three digits are 456. 456 ÷ 8 = 57. Therefore, 123456 is divisible by 8.
- 9876543: The last three digits are 543. 543 ÷ 8 = 67.875 (not a whole number). Therefore, 9876543 is not divisible by 8.
- 1000: The last three digits are 000, which is divisible by 8 (0 ÷ 8 = 0). Therefore, 1000 is divisible by 8.
This rule is based on the fact that 1000 is divisible by 8 (1000 = 8 * 125). Any number can be expressed as a sum of multiples of 1000 plus the last three digits. Since multiples of 1000 are divisible by 8, the divisibility depends solely on the last three digits.
Multiple sources confirm this rule: Byju's, CK-12, SplashLearn, and Cuemath.
