Divisibility Rule of 8
The divisibility rule of 8 helps us quickly determine if a number is divisible by 8 without performing full division. Instead of dividing the number, we just need to look at its last three digits. If the number formed by these last three digits is divisible by 8, then the whole number is divisible by 8.
Understanding the Rule
To check if a number is divisible by 8, follow these steps:
- Take the last three digits of the number.
- Check if this three-digit number is divisible by 8.
- If the three-digit number is divisible by 8, the entire number is divisible by 8. If not, it isn’t divisible by 8.
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For example:
- Number: 536
- Last three digits: 536
- 536 ÷ 8 = 67 (no remainder). So, 536 is divisible by 8.
- Number: 123456
- Last three digits: 456
- 456 ÷ 8 = 57 (no remainder). So, 123456 is divisible by 8.
Why Does the Rule Work?
The rule works because of how numbers are structured in place value. Any number can be broken down into a sum of digits multiplied by powers of 10. Since 10³ (1000) is divisible by 8, the divisibility of the entire number depends only on the last three digits. This is why we only need to focus on the last three digits to check divisibility by 8.
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Examples to Practice
- Number: 372
- Last three digits: 372
- 372 ÷ 8 = 46.5 (remainder). So, 372 is not divisible by 8.
- Number: 432
- Last three digits: 432
- 432 ÷ 8 = 54 (no remainder). So, 432 is divisible by 8.
Conclusion
The divisibility rule of 8 is a quick and simple way to determine if a number is divisible by 8. By just focusing on the last three digits, you can save time and avoid the need for lengthy division calculations. This rule is useful in everyday math problems, especially when dealing with large numbers.
FAQs on Divisibility Rule of 8
What is the divisibility rule of 8?
The divisibility rule of 8 states that a number is divisible by 8 if the number formed by its last three digits is divisible by 8. If the last three digits of the number are divisible by 8, the whole number is divisible by 8.
How do you use the divisibility rule of 8?
To use the rule, take the last three digits of the number and check if that three-digit number is divisible by 8. If it is, then the entire number is divisible by 8.
Can you give an example of the divisibility rule of 8?
Sure! Let’s take the number 123456. The last three digits are 456. Since 456 ÷ 8 = 57 (with no remainder), we know 123456 is divisible by 8.
Why do we only check the last three digits for divisibility by 8?
The rule works because the powers of 10 (like 1000, 10000, etc.) are divisible by 8. Therefore, we only need to focus on the last three digits to determine divisibility by 8.
Is the divisibility rule for 8 applicable to any number?
Yes, the divisibility rule of 8 can be applied to any integer. Just look at the last three digits of the number and check if they are divisible by 8.
What happens if the last three digits are not divisible by 8?
If the last three digits are not divisible by 8, then the entire number is not divisible by 8.
Can the divisibility rule of 8 be used with decimal numbers?
The divisibility rule of 8 is mainly used for whole numbers. It is not typically used for decimal numbers unless you are working with an integer portion and need to check divisibility.
How can I practice the divisibility rule of 8?
Practice by picking random numbers, focusing on the last three digits, and checking if they are divisible by 8. For example:
Number: 512
Last three digits: 512
512 ÷ 8 = 64, so 512 is divisible by 8.
Can you give a number that is not divisible by 8 using this rule?
Sure! Let’s take 372. The last three digits are 372. Since 372 ÷ 8 = 46.5 (with a remainder), 372 is not divisible by 8.
Is the divisibility rule for 8 the same for all number systems?
The divisibility rule for 8 specifically applies to the decimal system, which is the standard for most everyday math and calculations. Other number systems (binary, octal, etc.) would have their own rules for divisibility.