A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
Divisibility Rule of 8 Explained
The divisibility rule of 8 provides a quick way to determine if a number can be evenly divided by 8 without performing long division. This rule stems from the fact that 1000 is divisible by 8 (1000 = 8 * 125). Therefore, any number greater than 999 can be expressed as a multiple of 1000 plus its last three digits. If those last three digits are divisible by 8, then the entire number is also divisible by 8.
How to Check Divisibility by 8:
-
Identify the last three digits: Look at the last three digits of the number you want to check.
-
Check for divisibility by 8: Determine if the number formed by those last three digits is evenly divisible by 8.
-
Conclusion: If the number formed by the last three digits is divisible by 8, the entire number is also divisible by 8.
Examples:
-
Example 1: 3624
- The last three digits are 624.
- 624 ÷ 8 = 78
- Since 624 is divisible by 8, 3624 is also divisible by 8.
-
Example 2: 123456
- The last three digits are 456.
- 456 ÷ 8 = 57
- Since 456 is divisible by 8, 123456 is also divisible by 8.
-
Example 3: 98765432
- The last three digits are 432.
- 432 ÷ 8 = 54
- Since 432 is divisible by 8, 98765432 is also divisible by 8.
Why does this rule work?
Any number can be written in the form: Number = (Some Multiple of 1000) + (Last Three Digits).
Since 1000 is always divisible by 8, the divisibility by 8 depends only on the Last Three Digits.
