BrightChamps Logo
Hamburger Menu Icon for BrightChamps Website Navigation
Login
Creative Math Ideas Image
Live Math Learners Count Icon186 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Divisibility Rule of 105

Professor Greenline Explaining Math Concepts

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 105.

Divisibility Rule of 105 for US Students
Professor Greenline from BrightChamps

What is the Divisibility Rule of 105?

The divisibility rule for 105 is a method by which we can find out if a number is divisible by 105 or not without using the division method. A number is divisible by 105 if it is divisible by 3, 5, and 7 (since 105 = 3 × 5 × 7). 

 

Check whether 315 is divisible by 105 using the divisibility rule.

 

Step 1: Check divisibility by 3. The sum of the digits is 3 + 1 + 5 = 9, which is divisible by 3.


Step 2: Check divisibility by 5. The last digit is 5, which means it is divisible by 5.


Step 3: Check divisibility by 7. Double the last digit and subtract it from the rest of the number: 31 - (5 × 2) = 21, which is a multiple of 7.

 

Since 315 is divisible by 3, 5, and 7, it is divisible by 105.divisibility rule of 105
 

Professor Greenline from BrightChamps

Tips and Tricks for Divisibility Rule of 105

Learning the divisibility rules will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 105.

  • Know the multiples of 105: Memorize the multiples of 105 (105, 210, 315, 420, etc.) to quickly check divisibility. If a number meets all divisibility rules for 3, 5, and 7, it is divisible by 105.
     
  • Use the divisibility rules for 3, 5, and 7: Ensure you are familiar with each rule separately to apply them effectively for 105.
     
  • Repeat the process for large numbers: Students should keep repeating the divisibility process for each component (3, 5, and 7) until they confirm divisibility by all three.
     
  • 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 verify and also learn.
     
Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in Divisibility Rule of 105

The divisibility rule of 105 helps us quickly check if a given number is divisible by 105, but common mistakes like calculation errors can lead to incorrect results. Here, we will understand some common mistakes and how to avoid them.

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Not checking all divisibility rules.  

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Students should ensure they check divisibility by 3, 5, and 7 separately.

Max from BrightChamps Saying "Hey"

Divisibility Rule of 105 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

A shipment contains 525 boxes. Is the total number of boxes divisible by 105?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Yes, 525 is divisible by 105.

Explanation

To check the divisibility of 525 by 105, we need to confirm divisibility by 3, 5, and 7.

 
1) Check divisibility by 3: Sum of digits is 5 + 2 + 5 = 12, which is divisible by 3.


2) Check divisibility by 5: The last digit is 5, so it is divisible by 5.


3) Check divisibility by 7: Multiply the last digit by 2, 5 × 2 = 10. Subtract from the rest, 52 – 10 = 42, which is divisible by 7.


Since 525 is divisible by 3, 5, and 7, it is divisible by 105.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A farmer has 630 apples and wants to pack them equally into boxes that can hold a number of apples divisible by 105. Can he do this?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Yes, 630 apples can be packed equally into boxes divisible by 105.

Explanation

For 630 to be divisible by 105, it must be divisible by 3, 5, and 7.


1) Divisibility by 3: Sum of digits is 6 + 3 + 0 = 9, which is divisible by 3.


2) Divisibility by 5: The last digit is 0, so it is divisible by 5.


3) Divisibility by 7: Multiply the last digit by 2, 0 × 2 = 0. Subtract from the rest, 63 – 0 = 63, which is divisible by 7.
Since 630 is divisible by these three numbers, it is divisible by 105.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

A concert hall has 840 seats. Are the seats arranged in rows that are divisible by 105?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Yes, 840 seats can be arranged in rows divisible by 105.

Explanation

To check if 840 is divisible by 105, confirm divisibility by 3, 5, and 7.


1) Divisibility by 3: Sum of digits is 8 + 4 + 0 = 12, which is divisible by 3.


2) Divisibility by 5: The last digit is 0, so it is divisible by 5.


3) Divisibility by 7: Multiply the last digit by 2, 0 × 2 = 0. Subtract from the rest, 84 – 0 = 84, which is divisible by 7.
Thus, 840 is divisible by 105.
 

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

A company manufactures 945 widgets each week. Is this weekly production divisible by 105?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Yes, 945 is divisible by 105.

Explanation

 For 945 to be divisible by 105, it must be divisible by 3, 5, and 7.


1) Divisibility by 3: Sum of digits is 9 + 4 + 5 = 18, which is divisible by 3.


2) Divisibility by 5: The last digit is 5, so it is divisible by 5.


3) Divisibility by 7: Multiply the last digit by 2, 5 × 2 = 10. Subtract from the rest, 94 – 10 = 84, which is divisible by 7.


Therefore, 945 is divisible by 105.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

There are 1,155 chairs to be set up in a conference hall. Can the chairs be arranged in sections divisible by 105?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Yes, 1,155 can be arranged in sections divisible by 105.

Explanation

To determine if 1,155 is divisible by 105, we check divisibility by 3, 5, and 7.


1) Divisibility by 3: Sum of digits is 1 + 1 + 5 + 5 = 12, which is divisible by 3.


2) Divisibility by 5: The last digit is 5, so it is divisible by 5.


3) Divisibility by 7: Multiply the last digit by 2, 5 × 2 = 10. Subtract from the rest, 115 – 10 = 105, which is divisible by 7.


Thus, 1,155 is divisible by 105.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs on Divisibility Rule of 105

1.What is the divisibility rule for 105?

Math FAQ Answers Dropdown Arrow

2.How many numbers are there between 1 and 1000 that are divisible by 105?

Math FAQ Answers Dropdown Arrow

3.Is 420 divisible by 105?

Math FAQ Answers Dropdown Arrow

4.What if I meet only two of the divisibility rules?

Math FAQ Answers Dropdown Arrow

5.Does the divisibility rule of 105 apply to all integers?

Math FAQ Answers Dropdown Arrow

6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 105?

Math FAQ Answers Dropdown Arrow

7.What are some fun ways kids in United States can practice Divisibility Rule of 105 with numbers?

Math FAQ Answers Dropdown Arrow

8.What role do numbers and Divisibility Rule of 105 play in helping children in United States develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

9.How can families in United States create number-rich environments to improve Divisibility Rule of 105 skills?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for Divisibility Rule of 105

  • Divisibility rule: A set of rules used to determine if a number is divisible by another number without performing division.
     
  • Multiple: A product obtained by multiplying a number by an integer. For example, multiples of 105 are 105, 210, 315, etc.
     
  • Integer: A whole number that can be positive, negative, or zero.
     
  • Subtraction: The process of finding the difference between numbers by removing one from another.
     
  • Verification: The process of confirming the accuracy of a result, often by different means such as division.
     
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we believe numbers are more than symbols—they’re keys unlocking endless possibilities! Our goal is to help children across the United States build strong math skills, focusing today on the Divisibility Rule of 105 and especially on understanding the Divisibility Rule—delivered in a way that’s engaging, fun, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Disney World, keeping score during Little League games, or managing their allowance for the newest gadgets, knowing numbers boosts their confidence for real-life situations. Our hands-on lessons make learning enjoyable and straightforward. Since kids in the USA learn in diverse ways, we customize our approach to match each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps makes math relatable and exciting across America. Let’s make the Divisibility Rule an enjoyable part of every child’s math adventure!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom