142 LearnersLast updated on May 26th, 2025
Divisibility Rule of 353
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 353.
What is the Divisibility Rule of 353?
The divisibility rule for 353 is a method by which we can find out if a number is divisible by 353 or not without using the division method. Check whether 3530 is divisible by 353 with the divisibility rule.
Step 1: Multiply the last digit of the number by 106, here in 3530, 0 is the last digit, multiply it by 106. 0 × 106 = 0
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit, i.e., 353–0 = 353.
Step 3: As it is shown that 353 is a multiple of 353, therefore, the number is divisible by 353. If the result from step 2 isn't a multiple of 353, then the number isn't divisible by 353.
Tips and Tricks for Divisibility Rule of 353
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 353.
Know the multiples of 353:
Memorize the multiples of 353 (353, 706, 1059, ... etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 353, then the number is divisible by 353.
Use the negative numbers:
If the result we get after the subtraction is negative, we will avoid the symbol and consider it as positive for checking the divisibility of a number.
Repeat the process for large numbers:
Students should keep repeating the divisibility process until they reach a small number that is divisible by 353.
For example, check if 7060 is divisible by 353 using the divisibility test. Multiply the last digit by 106, i.e., 0 × 106 = 0. Subtract the remaining digits excluding the last digit by 0, 706–0 = 706. As 706 is a multiple of 353, 7060 is divisible by 353.
Use the division method to verify:
Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 353
The divisibility rule of 353 helps us to quickly check if the given number is divisible by 353, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which are multiplying the last digit by 106 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 353.
Divisibility Rule of 353 Examples
Problem 1
Divisibility Rule of 353 Examples
Yes, 706 is divisible by 353.
Explanation
To check if 706 is divisible by 353, apply the divisibility rule for 353:
1) Double the last two digits of the number, 06 × 2 = 12.
2) Subtract the result from the remaining digits, excluding the last two digits, 7 – 12 = -5.
3) Since -5 is not a multiple of 353, re-evaluate:
Add 353 to -5, resulting in 348, which indicates that 706 is divisible by 353.
Problem 2
Check the divisibility rule of 353 for 1412.
Yes, 1412 is divisible by 353.
Explanation
To determine if 1412 is divisible by 353:
1) Double the last two digits of the number, 12 × 2 = 24.
2) Subtract the result from the remaining digits, excluding the last two digits, 141 – 24 = 117.
3) Since 117 is not a multiple of 353 directly, continue:
Add 353 to 117, which results in 470.
Since 470 is not divisible by 353, re-check by subtraction and additive checks.
After adding another 353 (117 + 353 = 470), it becomes clear that 1412 is divisible by 353.
Problem 3
Is -353 divisible by 353?
Yes, -353 is divisible by 353.
Explanation
To check if -353 is divisible by 353:
1) Consider the positive form, 353, and apply the divisibility rule:
Double the last two digits, 53 × 2 = 106.
Subtract from the remaining number, 3 - 106 = -103.
Adjust by adding 353 to -103, resulting in 250, indicating divisibility.
2) Since the integer value of 353 is checked, -353 is divisible by 353.
Problem 4
Can 707 be divisible by 353 following the divisibility rule?
No, 707 isn't divisible by 353.
Explanation
To check if 707 is divisible by 353:
1) Double the last two digits of the number, 07 × 2 = 14.
2) Subtract the result from the remaining digits, excluding the last two digits, 7 – 14 = -7.
3) Since -7 is not a multiple of 353 and doesn't adjust to become one with simple addition, 707 is not divisible by 353.
Problem 5
Check the divisibility rule of 353 for 1765.
Yes, 1765 is divisible by 353.
Explanation
To verify if 1765 is divisible by 353:
1) Double the last two digits of the number, 65 × 2 = 130.
2) Subtract the result from the remaining digits, excluding the last two digits, 17 – 130 = -113.
3) Since -113 is not a multiple of 353 directly, add 353 to -113 to get 240, which confirms divisibility.
FAQs on Divisibility Rule of 353
1.What is the divisibility rule for 353?
2.How many numbers are there between 1 and 1000 that are divisible by 353?
3.Is 1059 divisible by 353?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 353 apply to all the integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 353?
7.What are some fun ways kids in United States can practice Divisibility Rule of 353 with numbers?
8.What role do numbers and Divisibility Rule of 353 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 353 skills?
Important Glossaries for Divisibility Rule of 353
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 353 if following the specific steps results in a multiple of 353.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example: multiples of 353 are 353, 706, 1059, etc.
- Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from another.
- Verification: Verification is the process of confirming the accuracy of a result using another method, such as division, to ensure correctness.
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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.
