200 LearnersLast updated on May 26th, 2025
Divisibility Rule of 89
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 89.
What is the Divisibility Rule of 89?
The divisibility rule for 89 is a method by which we can determine if a number is divisible by 89 without using the division method. Check whether 2673 is divisible by 89 with the divisibility rule.
Step 1: Multiply the last digit of the number by 9. Here in 2673, 3 is the last digit, so multiply it by 9. 3 × 9 = 27.
Step 2: Subtract the result from Step 1 from the remaining values, excluding the last digit. i.e., 267–27 = 240.
Step 3: Repeat the process for the result from Step 2. Multiply the last digit (0) by 9. 0 × 9 = 0. Subtract from the remaining number: 24–0 = 24.
Step 4: Since 24 is not a multiple of 89, 2673 is not divisible by 89. If the result from the repeated process is a multiple of 89, then the number is divisible by 89.
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Tips and Tricks for Divisibility Rule of 89
Learning the divisibility rule helps kids master division. Let’s learn a few tips and tricks for the divisibility rule of 89.
- Know the multiples of 89: Memorize the multiples of 89 (89, 178, 267, 356, 445, etc.) to quickly check divisibility. If the result from subtraction is a multiple of 89, then the number is divisible by 89.
- Use negative numbers: If the result we get after the subtraction is negative, we will avoid 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 89.
For example, check if 7125 is divisible by 89 using the divisibility test. Multiply the last digit by 9, i.e., 5 × 9 = 45. Subtract from the remaining digits excluding the last digit: 712–45 = 667.
Repeat the process: multiply the last digit (7) by 9, 7 × 9 = 63. Subtract from the remaining number: 66–63 = 3. Since 3 is not a multiple of 89, 7125 is not divisible by 89.
- 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 89
The divisibility rule of 89 helps us quickly check if a given number is divisible by 89, but common mistakes like calculation errors can lead to incorrect conclusions. 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, multiplying the last digit by 9 and then subtracting the result from the remaining digits excluding the last digit, and checking whether it is a multiple of 89.
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 result after subtraction. The process should be repeated until we get the smallest number that is divisible by 89.
Mistake 4
Not considering negative values.
Students often ignore negative values, thinking divisibility rules don't apply to them. 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 them. To avoid this error, students should practice regularly.
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Divisibility Rule of 89 Examples
Problem 1
Is 2678 divisible by 89?
No, 2678 is not divisible by 89.
Explanation
To check if 2678 is divisible by 89, we can use the divisibility rule of 89.
1) Separate the number into the last digit and the remaining number: 8 and 267.
2) Multiply the last digit by 9: 8 × 9 = 72.
3) Subtract this product from the remaining number: 267 - 72 = 195.
4) Check if 195 is a multiple of 89. No, 195 is not a multiple of 89.
Problem 2
Check the divisibility rule of 89 for 890.
Yes, 890 is divisible by 89.
Explanation
To verify the divisibility of 890 by 89:
1) Separate the number into the last digit and the remaining number: 0 and 89.
2) Multiply the last digit by 9: 0 × 9 = 0.
3) Subtract this product from the remaining number: 89 - 0 = 89.
4) Check if 89 is a multiple of 89. Yes, 89 is a multiple of 89 (89 × 1 = 89).
Problem 3
Is -3569 divisible by 89?
No, -3569 is not divisible by 89.
Explanation
To check if -3569 is divisible by 89, remove the negative sign and follow the rule:
1) Separate the number into the last digit and the remaining number: 9 and 356.
2) Multiply the last digit by 9: 9 × 9 = 81.
3) Subtract this product from the remaining number: 356 - 81 = 275.
4) Check if 275 is a multiple of 89. No, 275 is not a multiple of 89.
Problem 4
Can 712 be divisible by 89 following the divisibility rule?
No, 712 is not divisible by 89.
Explanation
To determine if 712 is divisible by 89:
1) Separate the number into the last digit and the remaining number: 2 and 71.
2) Multiply the last digit by 9: 2 × 9 = 18.
3) Subtract this product from the remaining number: 71 - 18 = 53.
4) Check if 53 is a multiple of 89. No, 53 is not a multiple of 89.
Problem 5
Check the divisibility rule of 89 for 8011.
Yes, 8011 is divisible by 89.
Explanation
To check the divisibility of 8011 by 89:
1) Separate the number into the last digit and the remaining number: 1 and 801.
2) Multiply the last digit by 9: 1 × 9 = 9.
3) Subtract this product from the remaining number: 801 - 9 = 792.
4) Check if 792 is a multiple of 89. Yes, 792 is a multiple of 89 (89 × 8 = 712).
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FAQs on Divisibility Rule of 89
1.What is the divisibility rule for 89?
2.How many numbers are there between 1 and 1000 that are divisible by 89?
3.Is 356 divisible by 89?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 89 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 89?
7.What are some fun ways kids in United States can practice Divisibility Rule of 89 with numbers?
8.What role do numbers and Divisibility Rule of 89 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 89 skills?
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Important Glossaries for Divisibility Rule of 89
- Divisibility rule: A set of rules used to find out whether a number is divisible by another number. For example, a number is divisible by 2 if the number ends with an even digit.
- Multiples: Multiples are the results obtained after multiplying a number by an integer. For example, multiples of 89 are 89, 178, 267, 356, etc.
- Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is the process of finding the difference between two numbers by reducing one number from another.
- Verification: The process of confirming the correctness of a calculation or result, often by using an alternative method 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.
