Divisibility Rule of 735
2026-02-28 10:55 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 735.

What is the Divisibility Rule of 735?

The divisibility rule for 735 is a method by which we can find out if a number is divisible by 735 or not without using the division method. To check whether a number is divisible by 735, it must be divisible by its prime factors: 5, 21, and 7 (since 735 = 5 × 21 × 7). 

For example, check whether 5145 is divisible by 735 using its prime factors:

Step 1: Check divisibility by 5. The last digit must be 0 or 5. Since 5145 ends in 5, it is divisible by 5.


Step 2: Check divisibility by 21. A number is divisible by 21 if it is divisible by both 3 and 7. 


- Check divisibility by 3: Sum the digits of 5145 (5+1+4+5=15), and since 15 is divisible by 3, so is 5145.


- Check divisibility by 7 using the rule: Double the last digit and subtract from the rest. 514-10=504, then repeat: 50-8=42. Since 42 is divisible by 7, 504, and hence 5145, is divisible by 7.


Step 3: Since 5145 is divisible by 5, 3, and 7, it is divisible by 735.

Tips and Tricks for Divisibility Rule of 735

Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 735.

Know the factors of 735:

Memorize that 735 = 5 × 21 × 7. For a number to be divisible by 735, it must be divisible by each of these factors.


Use divisibility rules for smaller factors:

If a number is divisible by 5, check for divisibility by 21 as a next step.


Repeat the process for large numbers:

Students should keep repeating the divisibility process until they reach a small number that is divisible by 735. For example, for a large number, first check divisibility by 5, then check divisibility by 21.


Use the division method to verify:

After using divisibility rules, verify your result with the division method for accuracy.

Common Mistakes and How to Avoid Them in Divisibility Rule of 735

The divisibility rule of 735 helps us quickly check if a given number is divisible by 735, but common mistakes like calculation errors lead to incorrect conclusions. Here are some mistakes and how to avoid them.

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Problem 1

Is 735 divisible by 735?

Okay, lets begin

Yes, 735 is divisible by 735.

Explanation

 Any number is divisible by itself, so 735 divided by 735 equals 1, which is an integer.

Well explained 👍

Problem 2

Can a box of 735 candies be evenly distributed among 735 children?

Okay, lets begin

Yes, the candies can be evenly distributed.

Explanation

If each child receives one candy, the total 735 candies are perfectly distributed among 735 children, with no leftover.

Well explained 👍

Problem 3

Is the number 1470 divisible by 735?

Okay, lets begin

Yes, 1470 is divisible by 735.

Explanation

1470 divided by 735 equals 2, which is an integer. Therefore, 1470 is divisible by 735.

Well explained 👍

Problem 4

Can a 735-page book be divided into volumes of 735 pages each?

Okay, lets begin

Yes, the book can be divided into volumes of 735 pages each.

Explanation

Since the total pages equal 735, dividing them into volumes of 735 pages results in one complete volume with no pages left over.

Well explained 👍

Problem 5

Does the number 2205 follow the divisibility rule for 735?

Okay, lets begin

Yes, 2205 is divisible by 735.

Explanation

2205 divided by 735 equals 3, which is an integer. Therefore, 2205 is divisible by 735

Well explained 👍

FAQs on Divisibility Rule of 735

1.What is the divisibility rule for 735?

The divisibility rule for 735 involves checking divisibility by its factors: 5 (last digit 0 or 5), 3 (sum of digits divisible by 3), and 7 (subtract twice the last digit from the rest).

2.How many numbers between 1 and 1000 are divisible by 735?

Only 1 number, which is 735 itself, is divisible by 735 between 1 and 1000.

3.Is 3675 divisible by 735?

Yes, 3675 is divisible by 735 because it satisfies divisibility by 5, 3, and 7.

4.What if I get 0 after checking a factor?

If you get 0 after checking a factor, it confirms divisibility by that factor.

5.Does the divisibility rule of 735 apply to all integers?

Yes, the divisibility rule of 735 applies to all integers.

Important Glossaries for Divisibility Rule of 735

  • Divisibility rule: A set of rules used to determine if one number is divisible by another.
     
  • Factors: Numbers that divide another number exactly without leaving a remainder.
     
  • Multiples: Results obtained by multiplying a number by an integer.
     
  • Integers: Whole numbers including positive, negative numbers, and zero.
     
  • Subtraction: The process of finding the difference between two numbers.

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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.