203 LearnersLast updated on May 26th, 2025
Divisibility Rule of 767
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 767.
What is the Divisibility Rule of 767?
The divisibility rule for 767 is a method by which we can find out if a number is divisible by 767 or not without using the division method. Check whether 7670 is divisible by 767 with the divisibility rule.
Step 1: Multiply the last three digits of the number by a specific multiplier, which in this case is 1. Here, in 7670, multiply 670 by 1. 670 × 1 = 670
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last three digits. i.e., 7 - 670 = -663.
Step 3: Since -663 is not a multiple of 767, the number is not divisible by 767. If the result from step 2 is a multiple of 767, then the number is divisible by 767.
Tips and Tricks for Divisibility Rule of 767
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 767.
- Know the multiples of 767: Memorize the multiples of 767 (767, 1534, 2301...etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 767, then the number is divisible by 767.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 767.
- 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 767
The divisibility rule of 767 helps us to quickly check if the given number is divisible by 767, but common mistakes like calculation errors lead to incorrect results. 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, which are multiplying the last three digits by the specific multiplier and then subtracting the result from the remaining digits excluding the last three digits, and checking whether it is a multiple of 767.
Mistake 2
Including the last three digits in subtraction.
Students should keep in mind that they should exclude the last three digits 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 as the result after subtraction. The process should be repeated until we get the smallest number that is divisible by 767.
Mistake 4
Confusing the steps.
Students often confuse the steps or forget the steps. To avoid the error, students should practice regularly.
Mistake 5
Not considering negative results.
Consider the absolute value of negative results when checking for divisibility.
Divisibility Rule of 767 Examples
Problem 1
Is 2301 divisible by 767?
No, 2301 is not divisible by 767.
Explanation
To determine if 2301 is divisible by 767, follow these steps:
1) Consider the last digit, 1, and multiply it by 7, resulting in 1 × 7 = 7.
2) Subtract this result from the remaining digits, 230 - 7 = 223.
3) Since 223 is not a multiple of 767, 2301 is not divisible by 767.
Problem 2
Check if 4602 follows the divisibility rule of 767.
Yes, 4602 is divisible by 767.
Explanation
To check the divisibility of 4602:
1) Take the last digit, 2, and multiply it by 7, which gives 2 × 7 = 14.
2) Subtract this from the remaining digits, 460 - 14 = 446.
3) Since 446 is not immediately recognizable as a multiple of 767, verify with division. 4602 divided by 767 equals exactly 6, confirming divisibility.
Problem 3
Is -1534 divisible by 767?
No, -1534 is not divisible by 767.
Explanation
To check divisibility for -1534:
1) Ignore the negative sign and use the last digit, 4, multiplying it by 7, resulting in 4 × 7 = 28.
2) Subtract this from the remaining digits, 153 - 28 = 125.
3) Since 125 is not a multiple of 767, -1534 is not divisible by 767.
Problem 4
Can 0 be divisible by 767 following the divisibility rule?
Yes, 0 is divisible by 767.
Explanation
Any number, including 0, divided by any non-zero integer results in 0, making 0 divisible by 767. There are no steps needed as 0 is universally divisible by all integers.
Problem 5
Check the divisibility rule of 767 for 7670.
Yes, 7670 is divisible by 767.
Explanation
To verify if 7670 is divisible by 767:
1) Take the last digit, 0, and multiply it by 7, which results in 0 × 7 = 0.
2) Subtract this from the remaining digits, 767 - 0 = 767.
3) Since 767 is clearly a multiple of 767, 7670 is divisible by 767.
FAQs on Divisibility Rule of 767
1.What is the divisibility rule for 767?
2.How many numbers are there between 1 and 10000 that are divisible by 767?
3.Is 3068 divisible by 767?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 767 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 767?
7.What are some fun ways kids in United States can practice Divisibility Rule of 767 with numbers?
8.What role do numbers and Divisibility Rule of 767 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 767 skills?
Important Glossaries for Divisibility Rule of 767
- 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 767 are 767, 1534, 2301, 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 confirming the accuracy of a result, often by using a different method like division to check the initial outcome.
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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.
