Divisibility Rule of 384
2026-02-28 00:44 Diff
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Last updated on August 5, 2025

The divisibility rule is a way to determine whether a number is divisible by another number without using the division method. In real life, we can use divisibility rules for quick math, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 384.

What is the Divisibility Rule of 384?

The divisibility rule for 384 helps us determine if a number is divisible by 384 without using the division method. To check whether a number is divisible by 384, we need to determine if it is divisible by 2, 3, and 8, as 384 is the product of these numbers (384 = 2^7 × 3).

Step 1: Check divisibility by 2. A number is divisible by 2 if its last digit is even.

Step 2: Check divisibility by 3. Add up all the digits of the number, and if the sum is divisible by 3, then the number is divisible by 3.

Step 3: Check divisibility by 8. A number is divisible by 8 if the last three digits form a number that is divisible by 8.

Example: Check whether 768 is divisible by 384.

Step 1: Check divisibility by 2. The last digit of 768 is 8, which is even, so it is divisible by 2.

Step 2: Check divisibility by 3. The sum of the digits of 768 is 7 + 6 + 8 = 21, and 21 is divisible by 3.

Step 3: Check divisibility by 8. The last three digits of 768 are 768, and 768 ÷ 8 = 96, which is an integer. Therefore, 768 is divisible by 8.

Since 768 is divisible by 2, 3, and 8, it is also divisible by 384.

Tips and Tricks for Divisibility Rule of 384

Learning the divisibility rule helps students master division. Let's explore a few tips and tricks for the divisibility rule of 384.

  • Understand the factors: Recognize that 384 is composed of the factors 2, 3, and 8. Ensure a number meets all these divisibility conditions.
     
  • Practice with multiples: Familiarize yourself with multiples of 384 (e.g., 384, 768, 1152) to quickly assess divisibility.
     
  • Double-check with smaller factors: If a number passes divisibility checks for 2, 3, and 8, it is divisible by 384.
     
  • Use the division method to verify: Students can use actual division to verify and cross-check their results, which helps reinforce their understanding.

Common Mistakes and How to Avoid Them in Divisibility Rule of 384

The divisibility rule of 384 allows us to quickly check if a number is divisible by 384, but common mistakes can occur. Here's how to avoid them:

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Problem 1

Is 1920 divisible by 384?

Okay, lets begin

Yes, 1920 is divisible by 384.

Explanation

To determine if 1920 is divisible by 384, follow these steps:  


1) Check if 1920 is divisible by 2. The last digit is 0, so it is divisible by 2.  


2) Check if 1920 is divisible by 3. Add the digits, 1 + 9 + 2 + 0 = 12, which is divisible by 3.  


3) Check if 1920 is divisible by 8. The last three digits are 920, which is not divisible by 8.  


Since the divisibility fails at step 3, 1920 is not divisible by 384.

Well explained 👍

Problem 2

Verify if 3072 is divisible by 384.

Okay, lets begin

Yes, 3072 is divisible by 384.

Explanation

To confirm divisibility of 3072 by 384, follow these steps:


1) Check if 3072 is divisible by 2. The last digit is 2, so it is divisible by 2.  


2) Check if 3072 is divisible by 3. Add the digits, 3 + 0 + 7 + 2 = 12, which is divisible by 3.  


3) Check if 3072 is divisible by 8. The last three digits are 072, and 72 is divisible by 8.  


Since all conditions are met, 3072 is divisible by 384.

Well explained 👍

Problem 3

Determine if 576 is divisible by 384.

Okay, lets begin

No, 576 is not divisible by 384.

Explanation

To check divisibility of 576 by 384, follow these steps:  


1) Check if 576 is divisible by 2. The last digit is 6, so it is divisible by 2.  


2) Check if 576 is divisible by 3. Add the digits, 5 + 7 + 6 = 18, which is divisible by 3.  


3) Check if 576 is divisible by 8. The last three digits are 576, and 576 divided by 8 is 72, which is divisible by 8.  


Since all conditions are met, 576 is divisible by 384.

Well explained 👍

Problem 4

Can 1536 be divisible by 384?

Okay, lets begin

Yes, 1536 is divisible by 384.

Explanation

To verify divisibility of 1536 by 384, follow these steps:  


1) Check if 1536 is divisible by 2. The last digit is 6, so it is divisible by 2.  


2) Check if 1536 is divisible by 3. Add the digits, 1 + 5 + 3 + 6 = 15, which is divisible by 3.  


3) Check if 1536 is divisible by 8. The last three digits are 536, and 536 divided by 8 is 67, which is divisible by 8.  


Since all conditions are met, 1536 is divisible by 384.

Well explained 👍

Problem 5

Check the divisibility rule of 384 for 2304.

Okay, lets begin

Yes, 2304 is divisible by 384.

Explanation

To determine if 2304 is divisible by 384, follow these steps:

 
1) Check if 2304 is divisible by 2. The last digit is 4, so it is divisible by 2.  


2) Check if 2304 is divisible by 3. Add the digits, 2 + 3 + 0 + 4 = 9, which is divisible by 3.  


3) Check if 2304 is divisible by 8. The last three digits are 304, and 304 divided by 8 is 38, which is divisible by 8.

 
Since all conditions are met, 2304 is divisible by 384.

Well explained 👍

FAQs on Divisibility Rule of 384

1.What is the divisibility rule for 384?

The divisibility rule for 384 requires checking if a number is divisible by 2, 3, and 8.

2.How many numbers between 1 and 1000 are divisible by 384?

There are 2 numbers between 1 and 1000 that are divisible by 384: 384 and 768.

3.Is 1152 divisible by 384?

Yes, because 1152 is a multiple of 384 (384 × 3 = 1152).

4.What if I get 0 after any calculation step?

If you get 0 after any calculation step, it confirms divisibility by that factor.

5.Does the divisibility rule of 384 apply to all integers?

Yes, the divisibility rule of 384 applies to all integers.

Important Glossaries for Divisibility Rule of 384

  • Divisibility rule: A set of guidelines used to determine if a number can be divided by another number without a remainder.
     
  • Factors: Numbers that divide another number exactly, without leaving a remainder.
     
  • Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 384 are 384, 768, 1152, etc.
     
  • Integer: A whole number that can be positive, negative, or zero.
     
  • Even numbers: Numbers that are divisible by 2 with no remainder, such as 2, 4, 6, etc.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.