Integers divisible by 8 are those that, based on the divisibility rule of 8, have their last three digits either as 000 or forming a number divisible by 8.
Here's a breakdown of how to determine if an integer is divisible by 8, based on the reference provided:
Divisibility Rule of 8
According to the divisibility rule, a given integer is divisible by 8 if the number formed by its last three digits is divisible by 8, or if those last three digits are 000.
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Last Three Digits as 000: Any integer ending in 000 is divisible by 8.
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Last Three Digits Divisible by 8: If the number formed by the last three digits is divisible by 8, then the whole integer is also divisible by 8.
Examples and Practical Insights:
- Example 1: The integer 1000 is divisible by 8 because its last three digits are 000.
- Example 2: The integer 123,456 is divisible by 8 because the last three digits, 456, form a number that is divisible by 8 (456 / 8 = 57).
- Example 3: The integer 987,655 is not divisible by 8 because the last three digits, 655, do not form a number divisible by 8. (655/8 = 81.875)
How to Check Divisibility by 8:
- Identify Last Three Digits: Look at the last three digits of the given integer.
- Check if 000: If these digits are 000, the number is divisible by 8.
- Divide by 8: If not 000, determine if the number formed by the last three digits is divisible by 8 using division. If it is divisible by 8 then the integer is also divisible by 8.
Practical Solutions:
- Mental Check: For smaller numbers, simple mental division can help.
- Calculator: For larger numbers, use a calculator to check if the last three digits are divisible by 8.
In summary, an integer is divisible by 8 if its last three digits are either 000, or when these digits form a number divisible by 8.
