142 LearnersLast updated on May 26th, 2025
Divisibility Rule of 167
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 167.
What is the Divisibility Rule of 167?
The divisibility rule for 167 is a method by which we can find out if a number is divisible by 167 or not without using the division method. Check whether 2501 is divisible by 167 with the divisibility rule.
Step 1: Multiply the last digit of the number by 5, here in 2501, 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., 250–5 = 245.
Step 3: As it is shown that 245 is not a multiple of 167, therefore, the number is not divisible by 167. If the result from step 2 is a multiple of 167, then the number is divisible by 167.
Tips and Tricks for Divisibility Rule of 167
Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 167.
- Know the multiples of 167: Memorize the multiples of 167 (167, 334, 501, 668, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 167, then the number is divisible by 167.
- 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 167.
For example: Check if 5012 is divisible by 167 using the divisibility test. Multiply the last digit by 5, i.e., 2 × 5 = 10.
Subtract the remaining digits excluding the last digit by 10, 501–10 = 491. Still, 491 is a large number, hence we will repeat the process again and multiply the last digit by 5, 1 × 5 = 5.
Now subtracting 5 from the remaining numbers excluding the last digit, 49–5 = 44. As 44 is not a multiple of 167, 5012 is not divisible by 167.
- 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 167
The divisibility rule of 167 helps us to quickly check if the given number is divisible by 167, 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 that are multiplying the last digit by 5 and then subtracting the result from the remaining digits excluding the last digits and checking whether it is a multiple of 167.
Divisibility Rule of 167 Examples
Problem 1
Is 1336 divisible by 167?
Yes, 1336 is divisible by 167.
Explanation
To check if 1336 is divisible by 167, we follow the divisibility rule:
1) Separate the last three digits: 336.
2) Subtract five times the last three digits from the remaining number: 1 - (5 × 336) = 1 - 1680 = -1679.
3) Check if the result is a multiple of 167. Since -1679 is not a multiple of 167, the calculation needs adjustment or confirmation. However, when checked directly, 1336 ÷ 167 = 8, a whole number, confirming divisibility.
Problem 2
Can 2501 be divisible by 167 following the divisibility rule?
No, 2501 is not divisible by 167.
Explanation
To check if 2501 is divisible by 167, we follow these steps:
1) Separate the last three digits: 501.
2) Subtract five times the last three digits from the remaining number: 2 - (5 × 501) = 2 - 2505 = -2503.
3) Check if the result is a multiple of 167. Since -2503 is not a multiple of 167, 2501 is not divisible by 167.
Problem 3
Check the divisibility rule of 167 for 167.
Yes, 167 is divisible by 167.
Explanation
Since 167 is the number itself, it is trivially divisible by 167. When dividing 167 by 167, the result is a whole number, 1.
Problem 4
Is 334 divisible by 167?
Yes, 334 is divisible by 167.
Explanation
To determine if 334 is divisible by 167:
1) Separate the last three digits: 334.
2) Subtract five times the last three digits from the remaining number: 0 - (5 × 334) = 0 - 1670 = -1670.
3) Check if the result is a multiple of 167. Since -1670 is not a straightforward multiple, directly checking 334 ÷ 167 gives 2, confirming divisibility.
Problem 5
Verify if 501 is divisible by 167.
No, 501 is not divisible by 167.
Explanation
To verify divisibility of 501 by 167:
1) Separate the last three digits: 501.
2) Since there are no preceding digits, we simply check if 501 is directly divisible by 167.
3) 501 ÷ 167 results in a non-integer, confirming that 501 is not divisible by 167.
FAQs on Divisibility Rule of 167
1.What is the divisibility rule for 167?
2.How many numbers are there between 1 and 1000 that are divisible by 167?
3.Is 501 divisible by 167?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 167 apply to all the integers?
6.How can children in Oman use numbers in everyday life to understand Divisibility Rule of 167?
7.What are some fun ways kids in Oman can practice Divisibility Rule of 167 with numbers?
8.What role do numbers and Divisibility Rule of 167 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve Divisibility Rule of 167 skills?
Important Glossaries for Divisibility Rule of 167
- 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 167 are 167, 334, 501, etc.
- Integers: Integers are the numbers that include all the 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 the correctness of a result or calculation, often by performing an additional method such as division to check divisibility.
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About BrightChamps in Oman
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.
