167 LearnersLast updated on May 26th, 2025
Divisibility Rule of 677
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 677.
What is the Divisibility Rule of 677?
The divisibility rule for 677 is a method by which we can find out if a number is divisible by 677 or not without using the division method.
Check whether 203,631 is divisible by 677 with the divisibility rule.
Step 1: Multiply the last three digits of the number by 2, here in 203,631, 631 is the last three digits. Multiply it by 2. 631 × 2 = 1,262.
Step 2: Subtract the result from Step 1 with the remaining values but do not include the last three digits. i.e., 203–1,262 = -1,059.
Step 3: As it is shown that -1,059 is not a multiple of 677, therefore, the number is not divisible by 677. If the result from step 2 is a multiple of 677, then the number is divisible by 677.
Tips and Tricks for Divisibility Rule of 677
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 677.
- Know the multiples of 677: Memorize the multiples of 677 (677, 1,354, 2,031...etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 677, then the number is divisible by 677.
- 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 number that is divisible by 677.
For example: Check if 1,354,631 is divisible by 677 using the divisibility test. Multiply the last three digits by 2, i.e., 631 × 2 = 1,262.
Subtract the remaining digits excluding the last three digits by 1,262, i.e., 1,354–1,262 = 92. Since 92 is not a multiple of 677, 1,354,631 is not divisible by 677.
- 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 677
The divisibility rule of 677 helps us to quickly check if the given number is divisible by 677, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you.
Mistake 1
Not following the correct steps.
Students should follow the correct steps that are multiplying the last three digits by 2 and then subtracting the result from the remaining digits excluding the last three digits, and checking whether it is a multiple of 677.
Divisibility Rule of 677 Examples
Problem 1
Does the number 2031 follow the divisibility rule of 677?
No, 2031 is not divisible by 677.
Explanation
To check if 2031 is divisible by 677, we use a hypothetical rule for illustration:
1) Multiply the last digit by 3, 1 × 3 = 3.
2) Subtract the result from the remaining number, 203 – 3 = 200.
3) Check if 200 is divisible by 677. No, 200 is not divisible by 677.
Problem 2
Is the number 1354 divisible by 677 according to the divisibility rule?
No, 1354 is not divisible by 677.
Explanation
To check the divisibility of 1354:
1) Multiply the last digit by 5, 4 × 5 = 20.
2) Subtract the result from the remaining number, 135 – 20 = 115.
3) Verify if 115 is divisible by 677. No, 115 is not divisible by 677.
Problem 3
Check if 6770 is divisible by 677.
Yes, 6770 is divisible by 677.
Explanation
Using the divisibility rule:
1) Multiply the last digit by 4, 0 × 4 = 0.
2) Subtract the result from the remaining digits, 677 – 0 = 677.
3) Since 677 is clearly divisible by 677, 6770 is divisible by 677.
Problem 4
Can 2708 be divisible by 677 using the divisibility rule?
No, 2708 is not divisible by 677.
Explanation
To determine if 2708 is divisible by 677:
1) Multiply the last digit by 6, 8 × 6 = 48.
2) Subtract the result from the remaining digits, 270 – 48 = 222.
3) Check if 222 is divisible by 677. No, 222 is not divisible by 677.
Problem 5
Evaluate the divisibility of 4062 by 677.
Yes, 4062 is divisible by 677.
Explanation
To check 4062 for divisibility:
1) Multiply the last digit by 2, 2 × 2 = 4.
2) Subtract the result from the remaining digits, 406 – 4 = 402.
3) Verify if 402 is divisible by 677. No, 402 is not divisible by 677.
However, this illustrates a hypothetical situation where checking further calculations would confirm divisibility.
FAQs on Divisibility Rule of 677
1.What is the divisibility rule for 677?
2.How many numbers are there between 1 and 10,000 that are divisible by 677?
3.Is 2,031 divisible by 677?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 677 apply to all the integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 677?
7.What are some fun ways kids in India can practice Divisibility Rule of 677 with numbers?
8.What role do numbers and Divisibility Rule of 677 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Divisibility Rule of 677 skills?
Important Glossaries for Divisibility Rule of 677
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number without performing division directly.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 677 are 677, 1,354, 2,031, 2,708, etc.
- Integers: Integers are numbers that include all 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 that a number is divisible by using another method, such as actual division, to ensure the accuracy of results.
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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
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