249 LearnersLast updated on May 26th, 2025
Divisibility Rule of 735
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.
Mistake 1
Not checking all factors.
Ensure you check divisibility by 5, 3, and 7 to determine divisibility by 735.
Mistake 2
Misapplying individual divisibility rules.
Review and correctly apply the rules for divisibility by 5, 3, and 7.
Mistake 3
Stopping at partial divisibility.
A number must be divisible by all factors of 735. Verify divisibility by each factor.
Mistake 4
Confusing the steps.
Practice regularly to memorize and correctly follow the steps for each factor's divisibility.
Mistake 5
Overlooking the use of the division method.
Use the division method to verify results and ensure accuracy.
Divisibility Rule of 735 Examples
Problem 1
Is 735 divisible by 735?
Yes, 735 is divisible by 735.
Explanation
Any number is divisible by itself, so 735 divided by 735 equals 1, which is an integer.
Problem 2
Can a box of 735 candies be evenly distributed among 735 children?
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.
Problem 3
Is the number 1470 divisible by 735?
Yes, 1470 is divisible by 735.
Explanation
1470 divided by 735 equals 2, which is an integer. Therefore, 1470 is divisible by 735.
Problem 4
Can a 735-page book be divided into volumes of 735 pages each?
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.
Problem 5
Does the number 2205 follow the divisibility rule for 735?
Yes, 2205 is divisible by 735.
Explanation
2205 divided by 735 equals 3, which is an integer. Therefore, 2205 is divisible by 735
FAQs on Divisibility Rule of 735
1.What is the divisibility rule for 735?
2.How many numbers between 1 and 1000 are divisible by 735?
3.Is 3675 divisible by 735?
4.What if I get 0 after checking a factor?
5.Does the divisibility rule of 735 apply to all integers?
6.How can children in Vietnam use numbers in everyday life to understand Divisibility Rule of 735?
7.What are some fun ways kids in Vietnam can practice Divisibility Rule of 735 with numbers?
8.What role do numbers and Divisibility Rule of 735 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Divisibility Rule of 735 skills?
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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About BrightChamps in Vietnam
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.
