What is the Test for Divisibility by 8?

S3-SA4-0043

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The Test for Divisibility by 8 is a quick way to check if a number can be divided by 8 without leaving any remainder. It states that a number is divisible by 8 if the number formed by its last three digits is divisible by 8.

Simple Example

Quick Example

Imagine you have 1240 cricket balls and you want to pack them into boxes that hold exactly 8 balls each. Instead of dividing 1240 by 8, you just look at the last three digits: 240. Since 240 is divisible by 8 (240 / 8 = 30), then 1240 is also divisible by 8.

Worked Example

Step-by-Step

Let's check if the number 5736 is divisible by 8.
1. Identify the last three digits of the number. For 5736, the last three digits form the number 736.
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2. Now, we need to check if 736 is divisible by 8.
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3. Divide 736 by 8: 736 / 8.
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4. 8 goes into 73 nine times (8 * 9 = 72). Subtract 72 from 73, which leaves 1.
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5. Bring down the next digit, 6, to make 16.
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6. 8 goes into 16 two times (8 * 2 = 16). Subtract 16 from 16, which leaves 0.
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7. Since 736 divided by 8 gives a remainder of 0 (736 / 8 = 92), 736 is divisible by 8.
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Therefore, 5736 is divisible by 8.

Why It Matters

Understanding divisibility rules helps you quickly simplify calculations, which is useful in many fields. In Computer Science, knowing if numbers are divisible by powers of 2 (like 8) is key for data storage and processing. Engineers use these concepts for efficient design and calculations, and even data scientists use patterns in numbers for analysis.

Common Mistakes

MISTAKE: Checking only the last two digits. | CORRECTION: For divisibility by 8, you MUST check the last THREE digits, not just two. Divisibility by 4 uses the last two digits.

MISTAKE: Forgetting that if the last three digits are 000, the number is divisible by 8. | CORRECTION: If the last three digits are 000 (e.g., 5000), the number formed by them (000) is divisible by 8, so the original number is also divisible by 8.

MISTAKE: Incorrectly dividing the last three digits by 8. | CORRECTION: Always perform the division of the last three digits by 8 carefully, either by long division or by breaking it down (e.g., 720 is 8 x 90, so 736 is 720 + 16, which is 8 x 90 + 8 x 2 = 8 x 92).

Practice Questions

Try It Yourself

QUESTION: Is 12344 divisible by 8? | ANSWER: Yes

QUESTION: Which of these numbers is NOT divisible by 8: 7800, 9128, 6542, 10000? | ANSWER: 6542

QUESTION: A mobile phone factory produced 45,672 phones. Can these phones be packed into boxes of 8 without any leftover? Explain using the divisibility test. | ANSWER: Yes. The last three digits of 45,672 form 672. 672 divided by 8 is 84 (672 = 8 x 84). Since 672 is divisible by 8, 45,672 is also divisible by 8.

MCQ

Quick Quiz

Which of the following numbers is divisible by 8?

3450

7164

9216

11234

The Correct Answer Is:

For 9216, the last three digits form 216. 216 divided by 8 is 27, so 216 is divisible by 8. Thus, 9216 is divisible by 8. For the other options, 450, 164, and 234 are not divisible by 8.

Real World Connection

In the Real World

Imagine you're a delivery person using a logistics app. The app might need to group packages efficiently for delivery routes. If a truck can hold a certain number of items, say, in multiples of 8, knowing divisibility by 8 helps the app quickly calculate if a specific load fits perfectly, saving time and fuel. This is similar to how inventory management systems in big e-commerce warehouses like Flipkart or Amazon check stock.

Key Vocabulary

Key Terms

DIVISIBILITY: The ability of one number to be divided by another number without a remainder. | REMAINDER: The amount left over after a division when one number does not divide another exactly. | DIGITS: The symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers. | MULTIPLE: The result of multiplying a number by an integer.

What's Next

What to Learn Next

Great job learning about divisibility by 8! Next, you can explore the 'Test for Divisibility by 9' and 'Test for Divisibility by 11'. These rules will help you become even faster at mental math and understanding number patterns.