170 LearnersLast updated on May 26th, 2025
Divisibility Rule of 223
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 223.
What is the Divisibility Rule of 223?
The divisibility rule for 223 is a method by which we can find out if a number is divisible by 223 or not without using the division method. Check whether 446 is divisible by 223 with the divisibility rule.
Step 1: Multiply the last digit of the number by 67, here in 446, 6 is the last digit, multiply it by 67. 6 × 67 = 402
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 44 - 402 = -358.
Step 3: Since -358 is not a multiple of 223, the number 446 is not divisible by 223. If the result from step 2 is a multiple of 223, then the number is divisible by 223.
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Tips and Tricks for Divisibility Rule of 223
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 223.
Know the multiples of 223:
Memorize the multiples of 223 (223, 446, 669, ...etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 223, then the number is divisible by 223.
Use the negative numbers:
If the result we get after the subtraction is negative, consider its absolute value 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 223.
For example: Check if 669 is divisible by 223 using the divisibility test.
Multiply the last digit by 67, i.e., 9 × 67 = 603.
Subtract the remaining digits excluding the last digit by 603, 66 - 603 = -537.
Since -537 is a multiple of 223, 669 is divisible by 223.
Use the division method to verify:
Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 223
The divisibility rule of 223 helps us to quickly check if the given number is divisible by 223, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which involve multiplying the last digit by 67 and then subtracting the result from the remaining digits excluding the last digit, and checking whether it is a multiple of 223.
Mistake 2
Including the last digit in subtraction.
Students should keep in mind that they should exclude the last digit while subtracting and include all the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have a large number after subtraction. The process should be repeated until we get the smallest number that is divisible by 223.
Mistake 4
Not considering the negative values.
Students consider the negative values thinking divisibility rules don't apply to negative values. But the divisibility rule is applicable for negative values too. So students should consider the negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps.
Students often confuse the steps or forget the steps; to avoid the error, students should practice regularly.
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Divisibility Rule of 223 Examples
Problem 1
Is 446 divisible by 223?
Yes, 446 is divisible by 223.
Explanation
To check if 446 is divisible by 223:
1) Divide 446 by 223.
2) 446 ÷ 223 = 2, with no remainder.
3) Since there is no remainder, 446 is divisible by 223.
Problem 2
Check the divisibility rule of 223 for 669.
Yes, 669 is divisible by 223.
Explanation
For checking the divisibility of 669 by 223:
1) Divide 669 by 223.
2) 669 ÷ 223 = 3, with no remainder.
3) Since there is no remainder, 669 is divisible by 223.
Problem 3
Is 1003 divisible by 223?
No, 1003 is not divisible by 223.
Explanation
To check if 1003 is divisible by 223:
1) Divide 1003 by 223.
2) 1003 ÷ 223 ≈ 4.5, with a remainder.
3) Since there is a remainder, 1003 is not divisible by 223.
Problem 4
Can 892 be divisible by 223 following the divisibility rule?
Yes, 892 is divisible by 223.
Explanation
To determine if 892 is divisible by 223:
1) Divide 892 by 223.
2) 892 ÷ 223 = 4, with no remainder.
3) Since there is no remainder, 892 is divisible by 223.
Problem 5
Check the divisibility rule of 223 for 2230.
Yes, 2230 is divisible by 223.
Explanation
To check divisibility of 2230 by 223:
1) Divide 2230 by 223.
2) 2230 ÷ 223 = 10, with no remainder.
3) Since there is no remainder, 2230 is divisible by 223.
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FAQs on Divisibility Rule of 223
1. What is the divisibility rule for 223?
2.How many numbers are there between 1 and 1000 that are divisible by 223?
3.Is 446 divisible by 223?
4.What if I get 0 after subtracting?
5. Does the divisibility rule of 223 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 223?
7.What are some fun ways kids in United States can practice Divisibility Rule of 223 with numbers?
8.What role do numbers and Divisibility Rule of 223 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 223 skills?
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Important Glossaries for Divisibility Rule of 223
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 223 if the calculated result is a multiple of 223.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 223 are 223, 446, 669, etc.
- Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from another.
- Absolute value: The absolute value of a number is the non-negative value of that number without regard to its sign. For example, the absolute value of both -537 and 537 is 537.
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About BrightChamps in United States
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.
