207 LearnersLast updated on May 26th, 2025
Divisibility Rule of 678
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 678.
What is the Divisibility Rule of 678?
The divisibility rule for 678 is a method by which we can find out if a number is divisible by 678 or not without using the division method.
Check whether 2034 is divisible by 678 with the divisibility rule.
Step 1: Check if 2034 is divisible by 2. Since the last digit is 4, which is even, 2034 is divisible by 2.
Step 2: Check if the sum of the digits (2 + 0 + 3 + 4 = 9) is divisible by 3. Since 9 is divisible by 3, 2034 is divisible by 3.
Step 3: Check if the number ends in 0, which would make it divisible by 10. Since it doesn't, 2034 is not divisible by 10, and hence not divisible by 678.
Tips and Tricks for Divisibility Rule of 678
Learning divisibility rules will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 678.
- Know the multiples of 678: Memorize the multiples of 678 (678, 1356, 2034...etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 678, then the number is divisible by 678.
- Use the divisibility rule for 2, 3, and 10: Since 678 is a composite number, it helps to check divisibility by 2, 3, and 10 first. A number must be divisible by all these to be divisible by 678.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 678.
For example, check if 2034 is divisible by 678 using the divisibility test. Since it fails the divisibility by 10, it is not divisible by 678.
- 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 678
The divisibility rule of 678 helps us to quickly check if a given number is divisible by 678, 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 checking all conditions.
Students should follow the correct steps that involve checking divisibility by 2, 3, and 10.
Mistake 2
Miscalculating the sum of digits for divisibility by 3.
Ensure the sum of the digits is calculated correctly when checking for divisibility by 3.
Mistake 3
Stopping the process after one check fails.
Remember to check all conditions, as divisibility by 678 requires divisibility by 2, 3, and 10.
Mistake 4
Not verifying with actual division.
Use the division method to verify results when in doubt.
Mistake 5
Confusing rules for different numbers.
Practice regularly to avoid confusion between rules for different numbers.
Divisibility Rule of 678 Examples
Problem 1
Is 678,000 divisible by 678?
Yes, 678,000 is divisible by 678.
Explanation
To check if 678,000 is divisible by 678, we can simplify the problem by checking the divisibility of 678 and 1,000 separately.
1) 1,000 is a multiple of 1,000, a factor of 678,000.
2) Given that 678 is a factor of itself, 678,000 is divisible by 678 because 678 × 1,000 = 678,000.
Problem 2
Can 1356 be divisible by 678?
Yes, 1356 is divisible by 678.
Explanation
To determine if 1356 is divisible by 678, we divide 1356 by 678 and check for a whole number.
1) Divide 1356 by 678, which equals 2.
2) Since the division results in a whole number, 1356 is divisible by 678 (678 × 2 = 1356).
Problem 3
Is 2034 a multiple of 678?
No, 2034 is not a multiple of 678.
Explanation
To see if 2034 is a multiple of 678, divide 2034 by 678.
1) Perform the division: 2034 ÷ 678 ≈ 3.000
2) The result is approximately 3, but not exact, indicating 2034 is not a multiple of 678.
Problem 4
Check if 4068 is divisible by 678.
Yes, 4068 is divisible by 678.
Explanation
To verify, divide 4068 by 678.
1) 4068 ÷ 678 = 6.
2) The division results in a whole number, confirming 4068 is divisible by 678 (678 × 6 = 4068).
Problem 5
Is -678 divisible by 678?
Yes, -678 is divisible by 678.
Explanation
To check the divisibility of -678 by 678, consider the absolute value.
1) |-678| ÷ 678 = 1.
2) Since the absolute division results in a whole number, -678 is divisible by 678.
FAQs on Divisibility Rule of 678
1.What is the divisibility rule for 678?
2.How many numbers are there between 1 and 1000 that are divisible by 678?
3.Is 1356 divisible by 678?
4.What if I get 0 after checking all conditions?
5.Does the divisibility rule of 678 apply to all the integers?
6.How can children in United Kingdom use numbers in everyday life to understand Divisibility Rule of 678?
7.What are some fun ways kids in United Kingdom can practice Divisibility Rule of 678 with numbers?
8.What role do numbers and Divisibility Rule of 678 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Divisibility Rule of 678 skills?
Important Glossaries for Divisibility Rule of 678
- 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 678 are 678, 1356, 2034...
- Composite number: A composite number is a positive integer that has at least one positive divisor other than one or itself.
- Integer: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
- Verification: The process of confirming the accuracy of a calculation or rule by using an alternative method, such as division.
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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.
