Divisibility Rule of 106
2026-02-28 10:25 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 performing actual division. In real life, divisibility rules help with quick calculations, dividing things evenly, and sorting. In this topic, we will learn about the divisibility rule of 106.

What is the Divisibility Rule of 106?

The divisibility rule for 106 is a method by which we can determine if a number is divisible by 106 without using the division method. Let's check whether 4242 is divisible by 106 using the divisibility rule.

Step 1: Separate the number into groups of three digits from the right. For 4242, we have two groups: 4 and 242.

Step 2: Multiply the leftmost group (4) by 1000 and the rightmost group (242) by 1. 4×1000=4000 and 242×1=242.

Step 3: Add the results: 4000+242=4242.

Step 4: Check if the sum (4242) is divisible by 106. If the result is divisible by 106, then the original number is also divisible by 106.
 

Tips and Tricks for Divisibility Rule of 106

Learning the divisibility rule will help kids master division. Let’s explore a few tips and tricks for the divisibility rule of 106.
 

  • Know the multiples of 106: Memorize multiples of 106 (106, 212, 318, 424, 530, etc.) to quickly check divisibility. If the result from the calculation is a multiple of 106, the number is divisible by 106.
     
  • Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This helps them verify and also learn.
     

Common Mistakes and How to Avoid Them in Divisibility Rule of 106

The divisibility rule of 106 helps us quickly check if a given number is divisible by 106. However, common mistakes can lead to incorrect results. Here are some common mistakes to avoid:

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Problem 1

Is 424 divisible by 106?

Okay, lets begin

No, 424 is not divisible by 106.

Explanation

To determine if 424 is divisible by 106, follow these steps:


1) Divide the number by 106 directly: 424 ÷ 106 = 4.


2) Check if the result is a whole number. Here, the result is 4, which means no remainder.


3) However, confirm by multiplying back: 106 × 4 = 424. Since the calculation checks out with no remainder, 424 is indeed divisible by 106.

Well explained 👍

Problem 2

Check the divisibility rule of 106 for 318.

Okay, lets begin

No, 318 is not divisible by 106.

Explanation

To verify divisibility by 106:


1) Divide 318 by 106: 318 ÷ 106 ≈ 3.


2) Check the remainder: 106 × 3 = 318, but 318 - 318 = 0 shows no remainder.


3) However, verify by multiplying back: 106 × 3 = 318. The remainder is zero, indicating divisibility.

Well explained 👍

Problem 3

Is 848 divisible by 106?

Okay, lets begin

Yes, 848 is divisible by 106.

Explanation

To check if 848 is divisible by 106:


1) Divide 848 by 106: 848 ÷ 106 = 8.


2) Check if the result is a whole number with no remainder. The result is 8, which confirms divisibility.


3) Verify by multiplying: 106 × 8 = 848. Since the calculation is correct, 848 is divisible by 106.

Well explained 👍

Problem 4

Can 742 be divisible by 106 following the divisibility rule?

Okay, lets begin

No, 742 is not divisible by 106.

Explanation

To check divisibility of 742 by 106:


1) Divide 742 by 106: 742 ÷ 106 ≈ 7.


2) Check the remainder: 742 - (106 × 7) = 742 - 742 = 0.


3) The remainder is zero, confirming divisibility.

Well explained 👍

Problem 5

Check the divisibility rule of 106 for 530.

Okay, lets begin

No, 530 is not divisible by 106.

Explanation

To determine if 530 is divisible by 106:


1) Divide 530 by 106: 530 ÷ 106 ≈ 5.


2) Calculate the remainder: 530 - (106 × 5) = 530 - 530 = 0.


3) The remainder is zero, indicating divisibility.

Well explained 👍

FAQs on Divisibility Rule of 106

1. What is the divisibility rule for 106?

The divisibility rule for 106 involves separating the number into groups of three digits from the right, multiplying each group by a power of ten, and adding the results. If the sum is divisible by 106, so is the number.

2.How many numbers are there between 1 and 1000 that are divisible by 106?

There are 9 numbers that can be divided by 106 between 1 and 1000. The numbers are 106, 212, 318, 424, 530, 636, 742, 848, 954

3. Is 530 divisible by 106?

Yes, because 530 is a multiple of 106 (106×5=530).
 

4. What if I get 0 after operations?

If you get 0 after performing the operations, it means the number is divisible by 106.
 

5.Does the divisibility rule of 106 apply to all integers?

Yes, the divisibility rule of 106 applies to all integers.

Important Glossaries for Divisibility Rule of 106

  • Divisibility rule: A set of guidelines to determine whether a number is divisible by another without performing division.
     
  • Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 106 are 106, 212, 318, etc.
     
  • Integers: Numbers that include all whole numbers, negative numbers, and zero.
     
  • Grouping: The process of dividing a number into smaller parts or groups, typically for easier calculation.
     

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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.