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137 LearnersLast updated on February 14th, 2025
Divisibility Rule of 563
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 563.
What is the Divisibility Rule of 563?
The divisibility rule for 563 is a method by which we can determine if a number is divisible by 563 without using the division method. Check whether 1689 is divisible by 563 with the divisibility rule.
Step 1: Multiply the last digit of the number by 2, here in 1689, 9 is the last digit, so multiply it by 2. 9 × 2 = 18
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 168–18 = 150.
Step 3: As 150 is not close to being a multiple of 563, repeat the process if necessary. If the result from Step 2 is a multiple of 563, then the number is divisible by 563. Otherwise, it is not.
Tips and Tricks for Divisibility Rule of 563
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 563.
- Know the multiples of 563: Memorize the multiples of 563 (563, 1126, 1689, ... etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 563, then the number is divisible by 563.
- Use negative numbers: If the result we get after the subtraction is negative, we will ignore 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 small number that is divisible by 563.
For example, check if 3372 is divisible by 563 using the divisibility test. Multiply the last digit by 2, i.e., 2 × 2 = 4. Subtract the remaining digits excluding the last digit by 4, 337–4 = 333.
Since 333 is not a multiple of 563, the original number is not divisible by 563.
- 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 563
The divisibility rule of 563 helps us quickly check if a given number is divisible by 563, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes that will help you to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which are multiplying the last digit by 2 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 563.
Divisibility Rule of 563 Examples
Problem 1
Is 1689 divisible by 563?
No, 1689 is not divisible by 563.
Explanation
To check if 1689 is divisible by 563, follow these steps:
1) Multiply the last digit of the number by a specific factor. Suppose we multiply 9 by 112 (a hypothetical factor for this example), 9 × 112 = 1008.
2) Subtract this result from the remaining digits excluding the last digit, 168 - 1008 = -840.
3) Check if the result is a multiple of 563. No, -840 is not a multiple of 563.
Problem 2
Check the divisibility rule of 563 for 2252.
No, 2252 is not divisible by 563.
Explanation
To determine if 2252 is divisible by 563, proceed as follows:
1) Multiply the last digit by a specific factor. Let's use 112 again for this example: 2 × 112 = 224.
2) Subtract this result from the remaining digits excluding the last digit, 225 - 224 = 1.
3) Check if 1 is a multiple of 563. No, 1 is not a multiple of 563.
Problem 3
Is -3378 divisible by 563?
No, -3378 is not divisible by 563.
Explanation
To check divisibility, ignore the negative sign and use the procedure:
1) Multiply the last digit by a factor, 8 × 112 = 896.
2) Subtract this from the remaining digits, 337 - 896 = -559.
3) Check if -559 is a multiple of 563. No, -559 is not a multiple of 563.
Problem 4
Can 4211 be divisible by 563 following the divisibility rule?
No, 4211 is not divisible by 563.
Explanation
To verify if 4211 is divisible by 563, use the method:
1) Multiply the last digit by a factor, 1 × 112 = 112.
2) Subtract this from the remaining digits, 421 - 112 = 309.
3) Check if 309 is a multiple of 563. No, 309 is not a multiple of 563.
Problem 5
Check the divisibility rule of 563 for 6749.
No, 6749 is not divisible by 563.
Explanation
To check divisibility, do the following:
1) Multiply the last digit by a factor, 9 × 112 = 1008.
2) Subtract this result from the remaining digits, 674 - 1008 = -334.
3) Verify if -334 is a multiple of 563. No, -334 is not a multiple of 563.
FAQs on Divisibility Rule of 563
1.What is the divisibility rule for 563?
2.Can you provide an example of a number divisible by 563?
3.Is 1126 divisible by 563?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 563 apply to all integers?
Important Glossaries for Divisibility Rule of 563
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number or not.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 563 are 563, 1126, 1689, etc.
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: The process of finding the difference between two numbers by reducing one number from another.
- Verification: A method of checking the correctness of a result, often by using an alternative calculation like 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.
