Divisibility Rule of 48
2026-02-28 10:57 Diff
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Last updated on August 5, 2025

The divisibility rule is a way to find out whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 48.

What is the Divisibility Rule of 48?

The divisibility rule for 48 is a method by which we can find out if a number is divisible by 48 or not without using the division method. Check whether 528 is divisible by 48 with the divisibility rule.

Step 1: Check if the number is divisible by both 3 and 16, as 48 is the product of these numbers (3 × 16 = 48).

Step 2: For divisibility by 3, add the digits of the number. If the sum is divisible by 3, then the number is divisible by 3. For 528, the sum of digits is 5 + 2 + 8 = 15, which is divisible by 3.

Step 3: For divisibility by 16, check the last four digits of the number (if there are fewer than four digits, check the entire number). Here, 528 is the number itself. 528 divided by 16 gives a whole number, confirming divisibility by 16.

Step 4: As 528 is divisible by both 3 and 16, it is divisible by 48.

Tips and Tricks for Divisibility Rule of 48

Learning the divisibility rule helps kids master division. Let's learn a few tips and tricks for the divisibility rule of 48.

  • Know the multiples of 48: Memorize the multiples of 48 (48, 96, 144, 192, 240, etc.) to quickly check the divisibility. If a number matches these multiples, it's divisible by 48.
     
  • Use the divisibility rules of factors: Since 48 is 3 × 16, confirming divisibility by both factors confirms divisibility by 48.
     
  • Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number. For example, check if 2496 is divisible by 48 using the divisibility test. Sum of digits: 2 + 4 + 9 + 6 = 21, divisible by 3. Last four digits 2496 divided by 16 gives a whole number, confirming divisibility by 16. Thus, 2496 is divisible by 48.
     
  • Use the division method to verify: Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.

Common Mistakes and How to Avoid Them in Divisibility Rule of 48

The divisibility rule of 48 helps us quickly check if a given number is divisible by 48, but common mistakes like calculation errors can lead to incorrect results. Here we will understand some common mistakes and how to avoid them.

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Problem 1

Is 576 divisible by 48?

Okay, lets begin

Yes, 576 is divisible by 48.

Explanation

To check if 576 is divisible by 48, we will use the divisibility rule for 48, which requires the number to be divisible by both 3 and 16.  


1) Check divisibility by 3: Sum the digits (5 + 7 + 6 = 18). Since 18 is divisible by 3, 576 is divisible by 3.  


2) Check divisibility by 16: The last four digits of 576 are 0576, which is simply 576. Since 576 divided by 16 equals 36, it is divisible by 16.  


Since 576 is divisible by both 3 and 16, it is divisible by 48.

Well explained 👍

Problem 2

Can 1,152 be divided evenly by 48?

Okay, lets begin

Yes, 1,152 is divisible by 48.

Explanation

To determine if 1,152 is divisible by 48, we again check for divisibility by 3 and 16.  


1) Check divisibility by 3: Sum the digits (1 + 1 + 5 + 2 = 9). Since 9 is divisible by 3, 1,152 is divisible by 3.  


2) Check divisibility by 16: The last four digits are 1152. Divide 1152 by 16, which equals 72, confirming it's divisible by 16.

 
Therefore, 1,152 is divisible by 48.

Well explained 👍

Problem 3

Is -384 divisible by 48?

Okay, lets begin

Yes, -384 is divisible by 48.

Explanation

We can ignore the negative sign and check the divisibility of 384.  


1) Check divisibility by 3: Sum the digits (3 + 8 + 4 = 15). Since 15 is divisible by 3, 384 is divisible by 3.  


2) Check divisibility by 16: The last four digits are 0384, which is 384. Divide 384 by 16, which equals 24, confirming it's divisible by 16.  


Since 384 is divisible by both 3 and 16, -384 is divisible by 48.

Well explained 👍

Problem 4

Can 934 be evenly divided by 48?

Okay, lets begin

No, 934 is not divisible by 48.

Explanation

 We need to check if 934 is divisible by both 3 and 16.  


1) Check divisibility by 3: Sum the digits (9 + 3 + 4 = 16). Since 16 is not divisible by 3, 934 is not divisible by 3, and therefore it cannot be divisible by 48.  


Thus, 934 is not divisible by 48.

Well explained 👍

Problem 5

Is 2,304 divisible by 48?

Okay, lets begin

Yes, 2,304 is divisible by 48.

Explanation

We will verify using divisibility by 3 and 16.  


1) Check divisibility by 3: Sum the digits (2 + 3 + 0 + 4 = 9). Since 9 is divisible by 3, 2,304 is divisible by 3.  


2) Check divisibility by 16: The last four digits are 2304. Divide 2304 by 16, which equals 144, confirming it's divisible by 16.

 
Therefore, 2,304 is divisible by 48.

Well explained 👍

FAQs on Divisibility Rule of 48

1.What is the divisibility rule for 48?

The divisibility rule for 48 involves checking if a number is divisible by both 3 and 16.

2.How many numbers between 1 and 1000 are divisible by 48?

There are 20 numbers that can be divided by 48 between 1 and 1000. The numbers are 48, 96, 144, 192, 240, 288, 336, 384, 432, 480, 528, 576, 624, 672, 720, 768, 816, 864, 912, 960.

3.Is 240 divisible by 48?

Yes, because 240 is a multiple of 48 (48 × 5 = 240).

4.Can the divisibility rule of 48 apply to negative numbers?

5.What if a number is divisible by 16 but not by 3?

If a number is divisible by 16 but not by 3, it is not divisible by 48.

Important Glossaries for Divisibility Rule of 48

  • Divisibility rule: A set of rules used to determine whether a number is divisible by another number. For example, a number is divisible by 2 if it ends with an even number.
     
  • Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 48 are 48, 96, 144, 192, etc.
     
  • Factors: Numbers that divide another number without leaving a remainder. For example, factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
     
  • Integers: Numbers that include all whole numbers, negative numbers, and zero.
     
  • Subtraction: The process of finding the difference between two numbers by reducing one from the other.

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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.