204 LearnersLast updated on May 26th, 2025
Divisibility Rule of 67
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 67.
What is the Divisibility Rule of 67?
The divisibility rule for 67 is a method by which we can find out if a number is divisible by 67 or not, without using the division method. Check whether 4021 is divisible by 67 with the divisibility rule.
Step 1: Multiply the last digit of the number by 5, here in 4021, 1 is the last digit, multiply it by 5. 1 × 5 = 5.
Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 402–5 = 397.
Step 3: As it is shown that 397 is not a multiple of 67, therefore, the number is not divisible by 67. If the result from step 2 is a multiple of 67, then the number is divisible by 67.
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Tips and Tricks for Divisibility Rule of 67
Learn the divisibility rule to help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 67.
Know the multiples of 67:
Memorize the multiples of 67 (67, 134, 201, 268, 335… etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 67, then the number is divisible by 67.
Use 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 67.
For example: Check if 13421 is divisible by 67 using the divisibility test.
Multiply the last digit by 5, i.e., 1 × 5 = 5.
Subtract the remaining digits excluding the last digit by 5, 1342–5 = 1337.
Still, 1337 is a large number, hence we will repeat the process again and multiply the last digit by 5, 7 × 5 = 35.
Now subtracting 35 from the remaining numbers excluding the last digit, 133–35 = 98.
Since 98 is not a multiple of 67, 13421 is not divisible by 67.
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 67
The divisibility rule of 67 helps us to quickly check if the given number is divisible by 67, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which are multiplying the last digit by 5 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 67.
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 got a large number as a result after subtraction. The process should be repeated until we get the smallest number that is divisible by 67.
Mistake 4
Not considering the negative values.
Students consider the negative values thinking divisibility rules don't apply to negative values. 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 the steps or forget the steps, to avoid the error students should practice regularly.
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Divisibility Rule of 67 Examples
Problem 1
Is 1340 divisible by 67?
Yes, 1340 is divisible by 67.
Explanation
To check if 1340 is divisible by 67, let's apply the divisibility rule.
1) Multiply the last digit by 5, 0 × 5 = 0.
2) Subtract the result from the remaining digits excluding the last digit, 134 – 0 = 134.
3) Check if 134 is a multiple of 67, yes, 134 is a multiple of 67 (67 × 2 = 134).
Problem 2
Can 2011 be divisible by 67 following the divisibility rule?
No, 2011 is not divisible by 67.
Explanation
To check if 2011 is divisible by 67, follow the steps:
1) Multiply the last digit by 5, 1 × 5 = 5.
2) Subtract the result from the remaining digits excluding the last digit, 201 – 5 = 196.
3) Check if 196 is a multiple of 67. No, 196 is not a multiple of 67.
Problem 3
Check the divisibility rule of 67 for 469.
Yes, 469 is divisible by 67.
Explanation
To check the divisibility rule of 67 for 469:
1) Multiply the last digit by 5, 9 × 5 = 45.
2) Subtract the result from the remaining digits excluding the last digit, 46 – 45 = 1.
3) Check if 1 is a multiple of 67. Yes, when the result is 0 or 1, it confirms divisibility.
Problem 4
Is -134 divisible by 67?
Yes, -134 is divisible by 67.
Explanation
To check if -134 is divisible by 67, ignore the negative sign:
1) Multiply the last digit by 5, 4 × 5 = 20.
2) Subtract the result from the remaining digits excluding the last digit, 13 – 20 = -7.
3) Check if the absolute value of -7 is a multiple of 67. When simplified, it confirms divisibility.
Problem 5
Check the divisibility rule of 67 for 3012.
No, 3012 is not divisible by 67.
Explanation
To check the divisibility rule of 67 for 3012:
1) Multiply the last digit by 5, 2 × 5 = 10.
2) Subtract the result from the remaining digits excluding the last digit, 301 – 10 = 291.
3) Check if 291 is a multiple of 67. No, 291 is not a multiple of 67.
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FAQs on Divisibility Rule of 67
1.What is the divisibility rule for 67?
2.How many numbers are there between 1 and 1000 that are divisible by 67?
3.Is 335 divisible by 67?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 67 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 67?
7.What are some fun ways kids in United States can practice Divisibility Rule of 67 with numbers?
8.What role do numbers and Divisibility Rule of 67 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 67 skills?
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- 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 67 are 67, 134, 201, 268, 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: The process of using another method, such as division, to confirm or cross-check the correctness of a solution.
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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.
