To determine if a large number is divisible by 8, you only need to check its last three digits.
Divisibility Rule of 8
The divisibility rule for 8 states that if the number formed by the last three digits of a number is divisible by 8, then the entire number is also divisible by 8. According to provided reference, you have to check if its last 3 digits are divisible by 8. If the last 3 digits are divisible by 8, then the whole number is also divisible by 8.
Explanation
This rule works because 1000 is divisible by 8 (1000 = 8 * 125). Therefore, any digits beyond the hundreds place will always be a multiple of 8, so they won't affect the divisibility. We only need to focus on the last three digits to determine if the entire number is divisible by 8.
Examples
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Example 1: Is 12856 divisible by 8?
- Check the last three digits: 856.
- Divide 856 by 8: 856 / 8 = 107 (no remainder).
- Therefore, 12856 is divisible by 8.
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Example 2: Is 97324 divisible by 8?
- Check the last three digits: 324.
- Divide 324 by 8: 324 / 8 = 40.5 (has a remainder).
- Therefore, 97324 is not divisible by 8.
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Example 3: Is 5000 divisible by 8?
- Check the last three digits: 000.
- 000 is considered divisible by 8.
- Therefore, 5000 is divisible by 8.
Why This Works
Any number can be represented as a sum of multiples of powers of 10. For example:
abcd = a * 1000 + b * 100 + c * 10 + d
Since 1000 is divisible by 8, a * 1000 will always be divisible by 8. The divisibility of the entire number by 8 then depends only on the divisibility of b * 100 + c * 10 + d, which is the number formed by the last three digits.
