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:

1. Take the last three digits of the number.
2. Check if this three-digit number is divisible by 8.
3. If the three-digit number is divisible by 8, the entire number is divisible by 8. If not, it isn’t divisible by 8.

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.

Also Check: Mutually Exclusive Events

Examples to Practice

1. Number: 372
   • Last three digits: 372
   • 372 ÷ 8 = 46.5 (remainder). So, 372 is not divisible by 8.
2. 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.