218 LearnersLast updated on May 26th, 2025
Divisibility Rule of 413
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 divisibility rules for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 413.
What is the Divisibility Rule of 413?
The divisibility rule for 413 is a method by which we can find out if a number is divisible by 413 or not without using the division method. Check whether 82600 is divisible by 413 with the divisibility rule.
Step 1: Multiply the last digit of the number by 124, here in 82600, 0 is the last digit, multiply it by 124. 0 × 124 = 0
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 8260 - 0 = 8260.
Step 3: As it is shown that 8260 is not a multiple of 413, therefore, the number is not divisible by 413. If the result from Step 2 is a multiple of 413, then the number is divisible by 413.
Tips and Tricks for Divisibility Rule of 413
Learning the divisibility rule can help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 413.
1. Know the multiples of 413:
Memorize the multiples of 413 (413, 826, 1239, 1652, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 413, then the number is divisible by 413.
2. Use the negative numbers:
If the result we get after the subtraction is negative, we will ignore the sign and consider it as positive for checking the divisibility of a number.
3. Repeat the process for large numbers:
Students should keep repeating the divisibility process until they reach a small number that is divisible by 413. For example, check if 165200 is divisible by 413 using the divisibility test.
Multiply the last digit by 124, i.e., 0 × 124 = 0.
Subtract the remaining digits excluding the last digit by 0, 16520 - 0 = 16520.
Still, 16520 is a large number, hence we will repeat the process again and multiply the last digit by 124, 0 × 124 = 0.
Now subtracting 0 from the remaining numbers excluding the last digit, 1652 - 0 = 1652.
As 1652 is a multiple of 413, 165200 is divisible by 413.
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 413
The divisibility rule of 413 helps us to quickly check if the given number is divisible by 413, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you understand.
Mistake 1
Not following the correct steps
Students should follow the correct steps that involve multiplying the last digit with 124 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 413.
Mistake 2
Including the last digit in subtraction.
Students should keep in mind that they should exclude the last digit while subtracting and include all the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have a large number resulting from subtraction. The process should be repeated until we get the smallest number that is divisible by 413.
Mistake 4
Not considering the negative values.
Students may ignore negative values thinking divisibility rules don't apply to them. But the divisibility rule is applicable for negative values too. So students should consider the negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps.
Students often confuse or forget the steps; to avoid this error, students should practice regularly.
Divisibility Rule of 413 Examples
Problem 1
Is the number 826 divisible by 413?
Yes, 826 is divisible by 413.
Explanation
To check if 826 is divisible by 413, we can follow these steps:
1) Divide 826 by 413 to see if it results in a whole number.
2) 826 ÷ 413 = 2, which is a whole number.
Therefore, 826 is divisible by 413.
Problem 2
Check if 1239 is divisible by 413.
Yes, 1239 is divisible by 413.
Explanation
To verify if 1239 is divisible by 413, perform the division:
1) Divide 1239 by 413.
2) 1239 ÷ 413 = 3.
Since the result is an integer, 1239 is divisible by 413.
Problem 3
Is -826 divisible by 413?
Yes, -826 is divisible by 413.
Explanation
To check divisibility, we can ignore the negative sign and follow the steps:
1) Divide the absolute value, 826, by 413.
2) 826 ÷ 413 = 2.
Since this division results in a whole number, -826 is divisible by 413.
Problem 4
Can 500 be divisible by 413?
No, 500 is not divisible by 413.
Explanation
To determine if 500 is divisible by 413, divide the number:
1) 500 ÷ 413 = 1.2116, which is not a whole number.
Therefore, 500 is not divisible by 413.
Problem 5
Check if 1652 is divisible by 413.
Yes, 1652 is divisible by 413.
Explanation
To check divisibility, divide 1652 by 413:
1) 1652 ÷ 413 = 4.
Since the result is a whole number, 1652 is divisible by 413.
FAQs on Divisibility Rule of 413
1.What is the divisibility rule for 413?
2.How many numbers are there between 1 and 5000 that are divisible by 413?
3. Is 826 divisible by 413?
4. What if I get 0 after subtracting?
5.Does the divisibility rule of 413 apply to all integers?
6.How can children in Thailand use numbers in everyday life to understand Divisibility Rule of 413?
7.What are some fun ways kids in Thailand can practice Divisibility Rule of 413 with numbers?
8.What role do numbers and Divisibility Rule of 413 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Divisibility Rule of 413 skills?
Important Glossary for Divisibility Rule of 413
- 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 2 if the number ends with even numbers.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 413 are 413, 826, 1239, 1652, etc.
- Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is the process of finding out the difference between two numbers by reducing one number from another.
- Verification: The process of confirming that the result obtained from applying the divisibility rule is correct, often done using direct division.
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About BrightChamps in Thailand
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.
