162 LearnersLast updated on May 26th, 2025
Divisibility Rule of 289
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 289.
What is the Divisibility Rule of 289?
The divisibility rule for 289 is a method by which we can find out if a number is divisible by 289 or not without using the division method. Check whether 83521 is divisible by 289 with the divisibility rule.
Step 1: Find the square root of 289, which is 17. Check if 83521 is divisible by 17 first.
Step 2: Use the divisibility rule of 17: Double the last digit and subtract it from the rest of the number. Repeat this process until you get a manageable number.
Step 3: As it is shown that 4913 is divisible by 17, therefore, the original number is divisible by 289. If the result from step 2 isn't a multiple of 17, then the number isn't divisible by 289.
Tips and Tricks for Divisibility Rule of 289
Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 289.
Know the multiples of 289:
Memorize multiples of 289 (289, 578, 867...etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 289, then the number is divisible by 289.
Use the negative numbers:
If the result we get after the subtraction is negative, 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 289. For example: Check if 83521 is divisible by 289 using the divisibility test. Use the rule for 17 on 83521.
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 289
The divisibility rule of 289 helps us to quickly check if the given number is divisible by 289, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps that involve checking divisibility by 17 first and then ensuring the number is divisible by 289.
Divisibility Rule of 289 Examples
Problem 1
Is 57841 divisible by 289?
Yes, 57841 is divisible by 289.
Explanation
To check if 57841 is divisible by 289, we use a hypothetical divisibility rule for 289:
1) Break the number into groups of three digits from the right: 057 and 841.
2) Calculate the difference between these groups: 841 - 057 = 784.
3) Check if 784 is divisible by 289. Yes, 784 is divisible by 289 (289 x 2.71 is approximately 784).
Problem 2
Check the divisibility of 86753 by 289.
No, 86753 is not divisible by 289.
Explanation
We use a hypothetical divisibility rule for 289:
1) Split the number into groups of three digits from the right: 086 and 753.
2) Calculate the difference between these groups: 753 - 086 = 667.
3) Check if 667 is divisible by 289. No, 667 is not divisible by 289 (289 x 2.31 is approximately 667).
Problem 3
Is -23112 divisible by 289?
Yes, -23112 is divisible by 289.
Explanation
To determine if -23112 is divisible by 289, we remove the negative sign and apply the divisibility rule:
1) Divide the number into groups of three digits from the right: 023 and 112.
2) Calculate the difference between these groups: 112 - 023 = 89.
3) Check if 89 is divisible by 289. No, but since we have a difference of zero when considering complete groups, the original number is effectively divisible by 289.
Problem 4
Can 459 be divisible by 289 following the divisibility rule?
No, 459 isn't divisible by 289.
Explanation
To check if 459 is divisible by 289 using a hypothetical rule:
1) Split the number into groups of three digits from the right: 000 and 459.
2) Calculate the difference between these groups: 459 - 000 = 459.
3) Check if 459 is a multiple of 289. No, 459 is not a multiple of 289 (289 x 1.59 is approximately 459).
Problem 5
Check the divisibility rule of 289 for 5780.
No, 5780 is not divisible by 289.
Explanation
To check the divisibility rule for 5780:
1) Divide the number into groups of three digits from the right: 005 and 780.
2) Calculate the difference between these groups: 780 - 005 = 775.
3) Check if 775 is a multiple of 289. No, 775 is not a multiple of 289 (289 x 2.68 is approximately 775).
FAQs on Divisibility Rule of 289
1.What is the divisibility rule for 289?
2.How many numbers are there between 1 and 1000 that are divisible by 289?
3. Is 578 divisible by 289?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 289 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 289?
7.What are some fun ways kids in United States can practice Divisibility Rule of 289 with numbers?
8.What role do numbers and Divisibility Rule of 289 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 289 skills?
Important Glossaries for Divisibility Rule of 289
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example: multiples of 289 are 289, 578, 867...
- Square root: A number which produces a specified quantity when multiplied by itself. For example, the square root of 289 is 17.
- Subtraction: Subtraction is a process of finding out the difference between two numbers, by reducing one number from another.
- Integers: Integers are the numbers that include all whole numbers, negative numbers, and zero.
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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.
