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143 LearnersLast updated on February 15th, 2025
Divisibility Rule of 684
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 684.
What is the Divisibility Rule of 684?
The divisibility rule for 684 is a method by which we can find out if a number is divisible by 684 or not without using the division method. Check whether 548,352 is divisible by 684 with the divisibility rule.
Step 1: Break the number into smaller components and check divisibility for each, such as checking divisibility by 2, 3, and 114 (since 684 = 2 × 3 × 114).
Step 2: Check for divisibility by 2: The last digit of 548,352 is 2, which is even, so it's divisible by 2.
Step 3: Check for divisibility by 3: Add the digits of 548,352 (5+4+8+3+5+2 = 27). Since 27 is divisible by 3, the number is divisible by 3.
Step 4: Check for divisibility by 114: This step requires ensuring the number is divisible by 114. You can check 548,352 ÷ 114 to see if the result is an integer.
Step 5: If the number is divisible by 2, 3, and 114, then it is divisible by 684.
Tips and Tricks for Divisibility Rule of 684
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 684.
- Know the components of 684: Understand that 684 is the product of 2, 3, and 114. This helps break down the problem.
- Use divisibility rules for smaller numbers: Apply the basic divisibility rules for 2 and 3 to narrow down the possibilities.
- Repeat the process for large numbers: Students should keep repeating the divisibility process for each component until they reach a conclusion.
- 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 684
The divisibility rule of 684 helps us quickly check if the given number is divisible by 684, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you.
Mistake 1
Not checking all components.
Ensure that you check divisibility by 2, 3, and 114 to confirm divisibility by 684.
Divisibility Rule of 684 Examples
Problem 1
Is 3,420 divisible by 684?
No, 3,420 is not divisible by 684.
Explanation
To determine if 3,420 is divisible by 684, let's break it down:
1) Identify if 3,420 is divisible by both 4 and 171 (since 684 = 4 × 171).
2) For divisibility by 4, the last two digits of 3,420 are 20, which is not divisible by 4.
3) Therefore, since 3,420 is not divisible by 4, it is not divisible by 684.
Problem 2
Check the divisibility rule of 684 for 6,840.
Yes, 6,840 is divisible by 684.
Explanation
To check if 6,840 is divisible by 684, follow these steps:
1) Verify if 6,840 is divisible by both 4 and 171.
2) The last two digits are 40, which is divisible by 4.
3) Now, check divisibility of 6,840 by 171.
4) Divide 6,840 by 171 and see if the result is an integer: 6,840 ÷ 171 = 40.
5) Since 40 is an integer, 6,840 is divisible by 684.
Problem 3
Is -9,108 divisible by 684?
Yes, -9,108 is divisible by 684.
Explanation
To check if -9,108 is divisible by 684:
1) Remove the negative sign and consider 9,108.
2) Check divisibility by 4: last two digits are 08, which is divisible by 4.
3) Check divisibility by 171: 9,108 ÷ 171 = 53.
4) Since 53 is an integer, 9,108 is divisible by 171 and therefore by 684.
Problem 4
Can 2,048 be divisible by 684 following the divisibility rule?
No, 2,048 is not divisible by 684.
Explanation
To test if 2,048 is divisible by 684:
1) Check if 2,048 is divisible by 4: last two digits are 48, divisible by 4.
2) Examine divisibility by 171: 2,048 ÷ 171 ≈ 11.98 (not an integer).
3) Since it doesn't result in an integer, 2,048 is not divisible by 684.
Problem 5
Check the divisibility rule of 684 for 136,800.
Yes, 136,800 is divisible by 684.
Explanation
To determine if 136,800 is divisible by 684:
1) Verify divisibility by 4: last two digits are 00, divisible by 4.
2) Check divisibility by 171: 136,800 ÷ 171 = 800.
3) Since 800 is an integer, 136,800 is divisible by 684.
FAQs on Divisibility Rule of 684
1.What is the divisibility rule for 684?
2.How many numbers are there between 1 and 1,000,000 that are divisible by 684?
3.Is 1,368 divisible by 684?
4.What if I get an integer after dividing by 114?
5.Does the divisibility rule of 684 apply to all integers?
Important Glossaries for Divisibility Rule of 684
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number without direct division.
- Components: Parts of a number used to simplify divisibility checks, such as 2, 3, and 114 for 684.
- Integers: Whole numbers, including positive, negative numbers, and zero.
- Subtraction: The process of finding the difference between two quantities.
- Multiples: The results obtained by multiplying a number by integers. For example, multiples of 684 include 684, 1,368, 2,052, etc.
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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.
