226 LearnersLast updated on May 26th, 2025
Divisibility Rule of 403
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 403.
What is the Divisibility Rule of 403?
The divisibility rule for 403 is a method by which we can find out if a number is divisible by 403 or not without using the division method. Check whether 1209 is divisible by 403 with the divisibility rule.
Step 1: Divide the number into smaller parts according to the digits of 403. Since 403 is a three-digit number, divide 1209 into parts: 1, 2, and 09.
Step 2: Multiply each of these parts by specific coefficients that correspond to the digits of 403. Here, multiply 1 by 4, 2 by 0, and 09 by 3.
Step 3: Add the results from step 2. If the sum is a multiple of 403, then the number is divisible by 403. If not, then the number isn't divisible by 403.
Tips and Tricks for Divisibility Rule of 403
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 403.
1. Know the multiples of 403:
Memorize the multiples of 403 (403, 806, 1209, ...) to quickly check the divisibility. If the result from the addition is a multiple of 403, then the number is divisible by 403.
2. Use the sum of coefficients:
If the result we get after the addition is large, we can use the sum of the original number's digits and compare it to the sum of 403's digits for a quick check.
3. Repeat the process for large numbers:
Students should keep repeating the divisibility process until they reach a small number that is divisible by 403. For example, check if 2418 is divisible by 403 using the divisibility test. Divide into parts: 2, 4, and 18. Multiply by coefficients: 2 × 4 = 8, 4 × 0 = 0, 18 × 3 = 54. Add the results: 8 + 0 + 54 = 62. Since 62 is not a multiple of 403, 2418 is not divisible by 403.
4. 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 to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 403
The divisibility rule of 403 helps us to quickly check if the given number is divisible by 403, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, dividing the number into parts, multiplying by coefficients, and then adding the results to check for divisibility by 403.
Mistake 2
Incorrect multiplication of parts.
Students should ensure they use the correct coefficients for each part when multiplying.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have got a large number. The process should be repeated until we get the smallest number that is divisible by 403.
Mistake 4
Confusing the steps
Students often confuse the steps or forget the steps. To avoid the error, students should practice regularly.
Divisibility Rule of 403 Examples
Problem 1
Is the number of pages in a book, 1209, divisible by 403?
Yes, 1209 is divisible by 403.
Explanation
To determine if 1209 is divisible by 403, we can perform the division directly since 403 is not a number with a commonly known divisibility rule like 7.
1) Divide 1209 by 403.
2) 1209 ÷ 403 = 3, with a remainder of 0.
3) Since the remainder is 0, 1209 is divisible by 403.
Problem 2
A library has a collection of 403 books. If each shelf must contain an equal number of books, can these books be evenly distributed on 5 shelves?
No, 403 books cannot be evenly distributed on 5 shelves.
Explanation
To check if 403 can be evenly divided by 5:
1) Divide 403 by 5.
2) 403 ÷ 5 = 80, with a remainder of 3.
3) Since there is a remainder, 403 books cannot be evenly distributed on 5 shelves.
Problem 3
A factory produces 2418 widgets in a day. Can these widgets be packed into boxes containing 403 widgets each without any leftover?
Yes, 2418 widgets can be packed into boxes containing 403 widgets each
Explanation
To check for divisibility:
1) Divide 2418 by 403.
2) 2418 ÷ 403 = 6, with a remainder of 0.
3) Since there is no remainder, 2418 is divisible by 403, meaning the widgets can be packed without leftovers.
Problem 4
During a competition, a score of 806 was achieved by a team. Is this score divisible by 403?
Yes, 806 is divisible by 403.
Explanation
To verify divisibility:
1) Divide 806 by 403.
2) 806 ÷ 403 = 2, with a remainder of 0.
3) Since the remainder is 0, 806 is divisible by 403.
Problem 5
A fleet of 1007 cars needs to be organized into groups, each containing 403 cars. Can this be done without leaving any cars ungrouped?
No, 1007 cars cannot be fully grouped into sets of 403.
Explanation
To determine if 1007 is divisible by 403:
1) Divide 1007 by 403.
2) 1007 ÷ 403 = 2, with a remainder of 201.
3) Since there is a remainder, 1007 is not divisible by 403, and cars will be left ungrouped.
FAQs on Divisibility Rule of 403
1.What is the divisibility rule for 403?
2. How many numbers are there between 1 and 2000 that are divisible by 403?
3. Is 1209 divisible by 403?
4. What if I get 0 after adding?
5. Does the divisibility rule of 403 apply to all integers?
6.How can children in Bahrain use numbers in everyday life to understand Divisibility Rule of 403?
7.What are some fun ways kids in Bahrain can practice Divisibility Rule of 403 with numbers?
8.What role do numbers and Divisibility Rule of 403 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Divisibility Rule of 403 skills?
Important Glossaries for Divisibility Rule of 403
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 403 are 403, 806, 1209, etc.
- Coefficients: In the context of divisibility rules, coefficients are numbers used to multiply parts of a number to simplify checking divisibility.
- Addition: Addition is the process of combining two or more numbers to get a total.
- Parts: In divisibility rules, parts refer to segments of a number divided based on the number of digits in the divisor.
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About BrightChamps in Bahrain
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.
