A number is divisible by 8 if the last three digits of the number are either zero or divisible by 8.
Here's why this works:
- Place Value: Numbers are built upon place values. The rightmost digit represents units, the next digit to the left represents tens, and so on.
- Multiples of 8: Every multiple of 8 is a multiple of 1000. This is because 1000 itself is divisible by 8 (1000 / 8 = 125).
- Last Three Digits: When you look at the last three digits of a number, you're essentially isolating the part that might be a multiple of 8 (since any higher place value is automatically a multiple of 1000, which is divisible by 8).
Examples:
- 56,344: The last three digits (344) are divisible by 8 (344 / 8 = 43). Therefore, 56,344 is also divisible by 8.
- 1,200: The last three digits (200) are divisible by 8 (200 / 8 = 25). Therefore, 1,200 is also divisible by 8.
- 3,000: The last three digits (000) are divisible by 8 (since they are zero). Therefore, 3,000 is also divisible by 8.
To quickly check if the last three digits are divisible by 8, you can:
- Divide by 8: If the division results in a whole number, the original number is divisible by 8.
- Mental Math: If you're familiar with multiples of 8, you can often quickly determine if the last three digits are divisible by 8 without performing a formal division.
Remember: This rule only works for checking divisibility by 8. For other numbers, different divisibility rules apply.
