How to Check Divisibility by 8

Oct 13, 2025 by miodeya.com 4 views

Introduction

In mathematics, divisibility is a fundamental concept that deals with the ability of a number to be divided by another number without leaving a remainder. In this article, we will focus on the divisibility rule for 8, which is a crucial concept in mathematics. We will determine if the given numbers are divisible by 8 and explore the underlying principles.

What is Divisibility by 8?

Divisibility by 8 is a rule that states a number is divisible by 8 if the number formed by its last three digits is divisible by 8. This rule is based on the fact that 8 is a factor of 1000, and any number that is a multiple of 1000 will also be a multiple of 8.

How to Check Divisibility by 8

To check if a number is divisible by 8, we need to follow these steps:

Take the last three digits of the number.
Check if the number formed by these three digits is divisible by 8.
If it is divisible, then the original number is also divisible by 8.

Example 1: 79104

Let's apply the divisibility rule to the number 79104.

Take the last three digits: 104
Check if 104 is divisible by 8: 104 ÷ 8 = 13 (with no remainder)
Since 104 is divisible by 8, the original number 79104 is also divisible by 8.

Example 2: 64000

Now, let's apply the divisibility rule to the number 64000.

Take the last three digits: 000
Check if 0 is divisible by 8: 0 ÷ 8 = 0 (with no remainder)
Since 0 is divisible by 8, the original number 64000 is also divisible by 8.

Example 3: 1387

Next, let's apply the divisibility rule to the number 1387.

Take the last three digits: 387
Check if 387 is divisible by 8: 387 ÷ 8 = 48.375 (with a remainder)
Since 387 is not divisible by 8, the original number 1387 is also not divisible by 8.

Example 4: 2564

Finally, let's apply the divisibility rule to the number 2564.

Take the last three digits: 564
Check if 564 is divisible by 8: 564 ÷ 8 = 70.5 (with a remainder)
Since 564 is not divisible by 8, the original number 2564 is also not divisible by 8.

Conclusion

In conclusion, the divisibility rule for 8 is a useful tool for determining if a number is divisible by 8. By following the steps outlined in this article, we can easily check if a number is divisible by 8. We have applied this rule to the given numbers and determined that 79104 and 64000 are divisible by 8, while 1387 and 2564 are not.

Frequently Asked Questions

Q: What is the divisibility rule for 8?

A: The divisibility rule for 8 states that a number is divisible by 8 if the number formed by its last three digits is divisible by 8.

Q: How do I check if a number is divisible by 8?

A: To check if a number is divisible by 8, take the last three digits of the number and check if the number formed by these three digits is divisible by 8.

Q: What if the number formed by the last three digits is not divisible by 8?

A: If the number formed by the last three digits is not divisible by 8, then the original number is also not divisible by 8.

Q: Can I use the divisibility rule for 8 to check if a number is divisible by other numbers?

A: No, the divisibility rule for 8 is specific to the number 8 and cannot be used to check if a number is divisible by other numbers.

Q: Are there any other divisibility rules that I should know about?

Frequently Asked Questions

Q: What is the divisibility rule for 8?

A: The divisibility rule for 8 states that a number is divisible by 8 if the number formed by its last three digits is divisible by 8.

Q: How do I check if a number is divisible by 8?

A: To check if a number is divisible by 8, take the last three digits of the number and check if the number formed by these three digits is divisible by 8.

Q: What if the number formed by the last three digits is not divisible by 8?

A: If the number formed by the last three digits is not divisible by 8, then the original number is also not divisible by 8.

Q: Can I use the divisibility rule for 8 to check if a number is divisible by other numbers?

A: No, the divisibility rule for 8 is specific to the number 8 and cannot be used to check if a number is divisible by other numbers.

Q: Are there any other divisibility rules that I should know about?

A: Yes, there are several other divisibility rules that you should know about, including the divisibility rules for 2, 3, 4, 5, 6, 7, 9, and 10.

Q: How do I determine if a number is divisible by 2?

A: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

Q: How do I determine if a number is divisible by 3?

A: A number is divisible by 3 if the sum of its digits is divisible by 3.

Q: How do I determine if a number is divisible by 4?

A: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Q: How do I determine if a number is divisible by 5?

A: A number is divisible by 5 if its last digit is 0 or 5.

Q: How do I determine if a number is divisible by 6?

A: A number is divisible by 6 if it is divisible by both 2 and 3.

Q: How do I determine if a number is divisible by 7?

A: A number is divisible by 7 if the difference between twice the digit at the units place and the number formed by the remaining digits is divisible by 7.

Q: How do I determine if a number is divisible by 9?

A: A number is divisible by 9 if the sum of its digits is divisible by 9.

Q: How do I determine if a number is divisible by 10?

A: A number is divisible by 10 if its last digit is 0.

Divisibility Rules Summary

Number	Divisibility Rule
2	Last digit is even (0, 2, 4, 6, or 8)
3	Sum of digits is divisible by 3
4	Last two digits are divisible by 4
5	Last digit is 0 or 5
6	Divisible by both 2 and 3
7	Difference between twice the digit at the units place and the number formed by the remaining digits is divisible by 7
8	Last three digits are divisible by 8
9	Sum of digits is divisible by 9
10	Last digit is 0

Conclusion

In conclusion, divisibility is a fundamental concept in mathematics that deals with the ability of a number to be divided by another number without leaving a remainder. The divisibility rules for 2, 3, 4, 5, 6, 7, 8, 9, and 10 are essential tools for determining if a number is divisible by these numbers. By understanding these rules, you can easily check if a number is divisible by these numbers and perform various mathematical operations.