182 LearnersLast updated on May 26th, 2025
Divisibility Rule of 561
The divisibility rule is a way to determine whether a number is divisible by another number without performing division directly. In real life, divisibility rules help with quick calculations, dividing items evenly, and organizing tasks. In this topic, we will explore the divisibility rule for 561.
What is the Divisibility Rule of 561?
The divisibility rule for 561 is a method to check if a number is divisible by 561 without dividing. Let's examine whether 1683 is divisible by 561 using this rule.
Step 1: Multiply the last digit of the number by a factor, specific to 561. (For example, if the factor is 3, multiply the last digit by 3.)
Here, in 1683, the last digit is 3. Multiply it by 3: 3 × 3 = 9.
Step 2: Subtract the result from Step 1 from the remaining number, excluding the last digit. For example, 168 - 9 = 159.
Step 3: Check if the result (159 in this case) is divisible by 561. If it is, then the original number is divisible by 561. If it's not, then the original number isn't divisible by 561.
Tips and Tricks for the Divisibility Rule of 561
Knowing the divisibility rule helps simplify division. Here are some tips and tricks for understanding the divisibility rule of 561:
- Memorize multiples of 561: Knowing the multiples of 561 can quickly confirm divisibility.
- Handle negative results: If the subtraction leads to a negative number, treat it as positive to check divisibility.
- Repeat the process for large numbers: Keep applying the divisibility process on large numbers until you reach a smaller number that is clearly divisible by 561.
- Verify with division: Use traditional division to cross-check and confirm results, enhancing understanding.
Common Mistakes and How to Avoid Them in the Divisibility Rule of 561
Understanding the divisibility rule of 561 can prevent errors, but common mistakes can occur. Here are some to watch out for:
Mistake 1
Skipping steps.
Follow each step carefully: multiply the last digit by the factor, subtract from the remaining digits, and check for divisibility.
Mistake 2
Including the last digit in subtraction.
Only exclude the last digit when subtracting; use the remaining digits.
Mistake 3
Not repeating the process for large numbers.
Continue the process until the result is a small number divisible by 561.
Mistake 4
Ignoring negative results.
Treat negative results as positive when checking divisibility.
Mistake 5
Confusing the steps.
Practice regularly to remember and correctly apply each step.
Divisibility Rule of 561 Examples
Problem 1
Is 1122 divisible by 561?
Yes, 1122 is divisible by 561.
Explanation
To check if 1122 is divisible by 561, we can apply the divisibility rule for 561. Since 561 is a composite number, we check divisibility by its prime factors (3, 11, and 17).
1) Check divisibility by 3: The sum of the digits is 1 + 1 + 2 + 2 = 6, which is divisible by 3.
2) Check divisibility by 11: The alternating sum of the digits is 1 - 1 + 2 - 2 = 0, which is divisible by 11.
3) Check divisibility by 17: 1122 ÷ 17 = 66, which is an integer, so 1122 is divisible by 17.
Since 1122 is divisible by 3, 11, and 17, it is divisible by 561.
Problem 2
Can 1683 be divisible by 561 using the divisibility rule?
Yes, 1683 is divisible by 561.
Explanation
We need to verify divisibility by the factors of 561, which are 3, 11, and 17.
1) Divisibility by 3: The sum of the digits is 1 + 6 + 8 + 3 = 18, which is divisible by 3.
2) Divisibility by 11: The alternating sum of the digits is 1 - 6 + 8 - 3 = 0, which is divisible by 11.
3) Divisibility by 17: 1683 ÷ 17 = 99, which is an integer, so 1683 is divisible by 17.
Since 1683 is divisible by 3, 11, and 17, it is divisible by 561.
Problem 3
Check the divisibility rule of 561 for -3366.
Yes, -3366 is divisible by 561.
Explanation
We remove the negative sign and check the divisibility by factors of 561: 3, 11, and 17.
1) Divisibility by 3: The sum of the digits is 3 + 3 + 6 + 6 = 18, which is divisible by 3.
2) Divisibility by 11: The alternating sum of the digits is 3 - 3 + 6 - 6 = 0, which is divisible by 11.
3) Divisibility by 17: 3366 ÷ 17 = 198, which is an integer, so 3366 is divisible by 17.
Since 3366 is divisible by 3, 11, and 17, it is divisible by 561.
Problem 4
Is 252 divisible by 561 using the divisibility rule?
No, 252 is not divisible by 561.
Explanation
We check divisibility by the factors of 561: 3, 11, and 17.
1) Divisibility by 3: The sum of the digits is 2 + 5 + 2 = 9, which is divisible by 3.
2) Divisibility by 11: The alternating sum of the digits is 2 - 5 + 2 = -1, which is not divisible by 11.
3) Divisibility by 17: 252 ÷ 17 = 14.8235, which is not an integer.
Since 252 is not divisible by 11 or 17, it is not divisible by 561.
Problem 5
Verify if 5610 is divisible by 561 using the rule.
Yes, 5610 is divisible by 561.
Explanation
We check divisibility by the factors of 561: 3, 11, and 17.
1) Divisibility by 3: The sum of the digits is 5 + 6 + 1 + 0 = 12, which is divisible by 3.
2) Divisibility by 11: The alternating sum of the digits is 5 - 6 + 1 - 0 = 0, which is divisible by 11.
3) Divisibility by 17: 5610 ÷ 17 = 330, which is an integer.
Since 5610 is divisible by 3, 11, and 17, it is divisible by 561.
FAQs on Divisibility Rule of 561
1.What is the divisibility rule for 561?
2.How many numbers between 1 and 1000 are divisible by 561?
3.Is 1122 divisible by 561?
4.What if I get 0 after subtracting?
5.Does the divisibility rule for 561 apply to all integers?
6.How can children in Saudi Arabia use numbers in everyday life to understand Divisibility Rule of 561?
7.What are some fun ways kids in Saudi Arabia can practice Divisibility Rule of 561 with numbers?
8.What role do numbers and Divisibility Rule of 561 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Divisibility Rule of 561 skills?
Important Glossary for the Divisibility Rule of 561
- Divisibility rule: A set of procedures to determine if one number is divisible by another without direct division.
- Multiples: Numbers obtained by multiplying a given number by an integer.
- Factor: A number that divides another number exactly without leaving a remainder.
- Integer: A whole number that can be positive, negative, or zero.
- Subtraction: The process of taking one number away from another to find the difference.
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About BrightChamps in Saudi Arabia
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.
