194 LearnersLast updated on May 26th, 2025
Divisibility Rule of 564
The divisibility rule is a way to determine whether a number is divisible by another number without using the division method. In real life, we can use divisibility rules for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 564.
What is the Divisibility Rule of 564?
The divisibility rule for 564 is a method by which we can find out if a number is divisible by 564 or not without using the division method. Check whether 1128 is divisible by 564 using this divisibility rule.
Step 1: Check if the number is divisible by 2, 3, and 47 (since 564 = 2 × 3 × 47).
Step 2: For divisibility by 2, the number should be even. 1128 is even.
Step 3: For divisibility by 3, the sum of the digits should be divisible by 3. The sum of the digits of 1128 is 1 + 1 + 2 + 8 = 12, which is divisible by 3.
Step 4: For divisibility by 47, you can divide the number by 47 directly or use a known method for checking divisibility by 47. For simplicity, we assume you know how to check divisibility by 47. In this case, 1128 ÷ 47 = 24, which is an integer.
Since 1128 is divisible by 2, 3, and 47, it is divisible by 564.
Tips and Tricks for Divisibility Rule of 564
Learning divisibility rules helps kids master division. Let’s learn a few tips and tricks for the divisibility rule of 564.
- Know the factors of 564: Memorize that 564 = 2 × 3 × 47 to quickly check divisibility.
- Use the divisibility rules of factors: Use the rules for 2, 3, and 47 to determine divisibility by 564.
- Repeat the process for large numbers: Keep using the divisibility rules for each factor until you verify divisibility by 564.
- Use the division method to verify: You can use the division method as a way to verify and cross-check your results.
Common Mistakes and How to Avoid Them in Divisibility Rule of 564
The divisibility rule of 564 helps us quickly check if a given number is divisible by 564, but common mistakes like calculation errors can lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Ensure that you check divisibility by each factor (2, 3, and 47) to confirm divisibility by 564.
Mistake 2
Forgetting the factors.
Remember that the factors of 564 are 2, 3, and 47, and apply their divisibility rules correctly.
Mistake 3
Not verifying with all factors.
Make sure to check divisibility by all three factors, not just one or two, to ensure the number is divisible by 564.
Mistake 4
Confusing the steps.
Students often confuse the steps or forget them. To avoid errors, students should practice regularly.
Mistake 5
Not repeating the process when the result is large.
Students often stop after checking once. The process should be repeated for each part until we confirm divisibility.
Divisibility Rule of 564 Examples
Problem 1
Is 1128 divisible by 564?
Yes, 1128 is divisible by 564.
Explanation
To check if 1128 is divisible by 564, we can use the divisibility rule.
1) Consider the number 1128 as two parts: 112 and 8.
2) Multiply the last part by 4, 8 × 4 = 32.
3) Add the result to the remaining part, 112 + 32 = 144.
4) Check if the result is a multiple of 564. Since 144 × 3.9167 = 564, 1128 is divisible by 564.
Problem 2
Check the divisibility rule of 564 for 1692.
Yes, 1692 is divisible by 564.
Explanation
To verify if 1692 is divisible by 564:
1) Divide 1692 into two parts: 169 and 2.
2) Multiply the last part by 4, 2 × 4 = 8.
3) Add the result to the remaining digits, 169 + 8 = 177.
4) Check if the result is a multiple of 564. Since 177 × 3.1864 = 564, 1692 is divisible by 564.
Problem 3
Is 282 divisible by 564?
No, 282 is not divisible by 564.
Explanation
To determine if 282 is divisible by 564:
1) Divide 282 into parts: 28 and 2.
2) Multiply the last part by 4, 2 × 4 = 8.
3) Add the result to the remaining digits, 28 + 8 = 36.
4) Check if the result is a multiple of 564. Since 36 is not a multiple of 564, 282 is not divisible by 564.
Problem 4
Can 2256 be divisible by 564 following the divisibility rule?
Yes, 2256 is divisible by 564.
Explanation
To check the divisibility of 2256 by 564:
1) Divide 2256 into two parts: 225 and 6.
2) Multiply the last part by 4, 6 × 4 = 24.
3) Add the result to the remaining digits, 225 + 24 = 249.
4) Check if the result is a multiple of 564. Since 249 × 2.2653 = 564, 2256 is divisible by 564.
Problem 5
Check the divisibility rule of 564 for 4512.
Yes, 4512 is divisible by 564.
Explanation
To confirm if 4512 is divisible by 564:
1) Divide 4512 into two parts: 451 and 2.
2) Multiply the last part by 4, 2 × 4 = 8.
3) Add the result to the remaining digits, 451 + 8 = 459.
4) Check if the result is a multiple of 564. Since 459 × 1.2283 = 564, 4512 is divisible by 564.
FAQs on Divisibility Rule of 564
1.What is the divisibility rule for 564?
2.How do you check if a number is divisible by 47?
3.Is 1128 divisible by 564?
4.What if one of the factors does not divide?
5.Do these rules apply to negative numbers?
6.How can children in Philippines use numbers in everyday life to understand Divisibility Rule of 564?
7.What are some fun ways kids in Philippines can practice Divisibility Rule of 564 with numbers?
8.What role do numbers and Divisibility Rule of 564 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Divisibility Rule of 564 skills?
Important Glossary for Divisibility Rule of 564
- Divisibility rule: A set of rules used to determine whether a number is divisible by another number.
- Factors: Numbers that are multiplied together to get another number. For example, the factors of 564 are 2, 3, and 47.
- Even number: A number divisible by 2 without a remainder.
- Integer: A whole number that can be positive, negative, or zero.
- Sum of digits: The total obtained by adding all the digits of a number together.
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About BrightChamps in Philippines
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.
