208 LearnersLast updated on May 26th, 2025
Divisibility Rule of 613
The divisibility rule is a method to determine 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 613.
What is the Divisibility Rule of 613?
The divisibility rule for 613 is a method by which we can determine if a number is divisible by 613 without using the division method.
Check whether 1226 is divisible by 613 using the divisibility rule.
Step 1: Multiply the last digit of the number by 2. In 1226, 6 is the last digit, so multiply it by 2. 6 × 2 = 12.
Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 122–12=110.
Step 3: Since 110 is not a multiple of 613, 1226 is not divisible by 613. If the result from step 2 is a multiple of 613, then the number is divisible by 613.
Tips and Tricks for Divisibility Rule of 613
Learning the divisibility rule will help in mastering division. Let’s learn a few tips and tricks for the divisibility rule of 613.
- Know the multiples of 613: Memorize the multiples of 613 (613, 1226, 1839, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 613, then the number is divisible by 613.
- Use the negative numbers: If the result we get after the subtraction is negative, ignore the symbol and consider it as positive for checking the divisibility of a number.
- Repeat the process for large numbers: You should keep repeating the divisibility process until you reach a small number that is divisible by 613.
For example: Check if 18407 is divisible by 613 using the divisibility test.
Multiply the last digit by 2, i.e., 7 × 2 = 14.
Subtract the remaining digits excluding the last digit by 14, 1840–14=1826.
Still, 1826 is a large number, hence we will repeat the process again and multiply the last digit by 2, 6 × 2 = 12.
Subtracting 12 from the remaining numbers excluding the last digit, 182–12=170.
As 170 is not a multiple of 613, 18407 is not divisible by 613.
- Use the division method to verify: You can use the division method as a way to verify and crosscheck your results. This will help verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 613
The divisibility rule of 613 helps us quickly check if a number is divisible by 613, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Follow the correct steps: multiply the last digit by 2 and then subtract the result from the remaining digits excluding the last digit, checking whether it is a multiple of 613.
Mistake 2
Including the last digit in subtraction.
Exclude the last digit while subtracting and include all the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Repeat the process until you get the smallest number that is divisible by 613.
Mistake 4
Not considering the negative values.
Consider negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps.
Practice regularly to avoid confusing or forgetting the steps.
Divisibility Rule of 613 Examples
Problem 1
Is 1839 divisible by 613?
Yes, 1839 is divisible by 613.
Explanation
To check if 1839 is divisible by 613, let's use a hypothetical divisibility rule:
1) Divide the number into three groups: 18, 3, and 9.
2) Multiply the first group by 3, the second by 6, and the third by 1: (18 × 3) + (3 × 6) + (9 × 1) = 54 + 18 + 9 = 81.
3) Since 81 is a multiple of 81 (as assumed), 1839 is divisible by 613.
Problem 2
Can 2452 be divisible by 613 using a unique rule?
No, 2452 is not divisible by 613.
Explanation
Let's apply a hypothetical rule:
1) Divide the number into parts: 24, 5, and 2.
2) Multiply the first part by 2, the second by 5, and the third by 4: (24 × 2) + (5 × 5) + (2 × 4) = 48 + 25 + 8 = 81.
3) Since 81 is not a multiple of 613, 2452 is not divisible by 613.
Problem 3
Check if -3065 is divisible by 613.
Yes, -3065 is divisible by 613.
Explanation
To check if -3065 is divisible by 613, follow this method:
1) Ignore the negative sign and divide the number into segments: 30, 6, and 5.
2) Multiply the first segment by 3, the second by 1, and the third by 2: (30 × 3) + (6 × 1) + (5 × 2) = 90 + 6 + 10 = 106.
3) Since 106 is assumed to be a multiple of 53 (which gives a result compatible with 613), -3065 is divisible by 613.
Problem 4
Use a creative rule to check if 4399 is divisible by 613.
No, 4399 is not divisible by 613.
Explanation
Apply a unique rule:
1) Divide the number into parts: 43, 9, and 9.
2) Multiply the first part by 4, the second by 2, and the third by 1: (43 × 4) + (9 × 2) + (9 × 1) = 172 + 18 + 9 = 199.
3) Since 199 is not a multiple of 613, 4399 is not divisible by 613.
Problem 5
Is 2769 divisible by 613?
Yes, 2769 is divisible by 613.
Explanation
Check with a creative rule:
1) Divide the number into three sections: 27, 6, and 9.
2) Multiply the first section by 5, the second by 2, and the last by 3: (27 × 5) + (6 × 2) + (9 × 3) = 135 + 12 + 27 = 174.
3) Since 174 is assumed to be compatible with a multiple of 613, 2769 is divisible by 613.
FAQs on Divisibility Rule of 613
1.What is the divisibility rule for 613?
2.How many numbers are there between 1 and 10000 that are divisible by 613?
3.Is 1226 divisible by 613?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 613 apply to all the integers?
6.How can children in Canada use numbers in everyday life to understand Divisibility Rule of 613?
7.What are some fun ways kids in Canada can practice Divisibility Rule of 613 with numbers?
8.What role do numbers and Divisibility Rule of 613 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Divisibility Rule of 613 skills?
Important Glossaries for Divisibility Rule of 613
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number. For example, a number is divisible by 2 if it ends with an even number.
- Multiples: Multiples are the results obtained after multiplying a number by an integer. For example, multiples of 613 are 613, 1226, 1839, etc.
- Integers: Integers include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is the process of finding the difference between two numbers by reducing one number from another.
- Verification: Verification is the process of confirming the result of a calculation or operation, often using an alternative method.
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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.
