196 LearnersLast updated on May 26th, 2025
Divisibility Rule of 189
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 189.
What is the Divisibility Rule of 189?
The divisibility rule for 189 is a method by which we can find out if a number is divisible by 189 or not without using the division method. Check whether 1701 is divisible by 189 with the divisibility rule.
Step 1: Check if the number is divisible by 9. Add the digits of the number, and if the sum is divisible by 9, then the number is divisible by 9. For 1701, 1+7+0+1=9, which is divisible by 9.
Step 2: Check if the number is divisible by 21. Check if the number is divisible by both 3 and 7. For 1701, the sum of the digits is 9, which is divisible by 3, and for 7, subtract twice the last digit from the rest of the number (170-2*1=168), which is divisible by 7.
Step 3: Since 1701 is divisible by both 9 and 21, it is divisible by 189.
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Tips and Tricks for Divisibility Rule of 189
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 189.
- Know the multiples of 189: Memorize the multiples of 189 (189, 378, 567, 756…etc.) to quickly check for divisibility.
- Use the divisibility rules for 9 and 21: Check if a number is divisible by 9 and 21; if both conditions are met, the number is divisible by 189.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 189. For example: Check if 3402 is divisible by 189. First, check for divisibility by 9: 3+4+0+2=9, which is divisible by 9. Then check for divisibility by 21: 340-2*2=336, which is divisible by 21.
- 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 189
The divisibility rule of 189 helps us to quickly check if the given number is divisible by 189, 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 by checking divisibility by 9 and 21.
Mistake 2
Assuming divisibility by one rule is enough.
Remember, both rules need to be satisfied for divisibility by 189.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have got a large number. The process should be repeated until we get the smallest number that is divisible by 189.
Mistake 4
Confusing divisibility rules for different numbers.
Students often confuse the steps or forget the steps, to avoid the error students should practice regularly.
Mistake 5
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Divisibility Rule of 189 Examples
Problem 1
Is 378 divisible by 189?
Yes, 378 is divisible by 189.
Explanation
To determine if 378 is divisible by 189, follow these steps:
1) Divide 378 by 189, which results in 2.
2) If the result is an integer, then 378 is divisible by 189.
3) Since 2 is an integer, 378 is divisible by 189.
Problem 2
Check the divisibility rule of 189 for 567.
Yes, 567 is divisible by 189.
Explanation
To check if 567 is divisible by 189:
1) Divide 567 by 189, resulting in 3.
2) If the result is an integer, then 567 is divisible by 189.
3) Since 3 is an integer, 567 is divisible by 189.
Problem 3
Is 945 divisible by 189?
Yes, 945 is divisible by 189.
Explanation
To verify if 945 is divisible by 189:
1) Divide 945 by 189, which results in 5.
2) If the result is an integer, then 945 is divisible by 189.
3) Since 5 is an integer, 945 is divisible by 189.
Problem 4
Can 1235 be divisible by 189 following the divisibility rule?
No, 1235 is not divisible by 189.
Explanation
To determine if 1235 is divisible by 189:
1) Divide 1235 by 189, resulting in approximately 6.53.
2) If the result is not an integer, then 1235 is not divisible by 189.
3) Since 6.53 is not an integer, 1235 is not divisible by 189.
Problem 5
Check the divisibility rule of 189 for 1890.
Yes, 1890 is divisible by 189.
Explanation
To check if 1890 is divisible by 189:
1) Divide 1890 by 189, which results in 10.
2) If the result is an integer, then 1890 is divisible by 189.
3) Since 10 is an integer, 1890 is divisible by 189.
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FAQs on Divisibility Rule of 189
1.What is the divisibility rule for 189?
2.How many numbers are there between 1 and 1000 that are divisible by 189?
3.Is 567 divisible by 189?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 189 apply to all the integers?
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Important Glossaries for Divisibility Rule of 189
- 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 189 are 189, 378, 567, etc.
- Integers: Integers are numbers that include all the whole numbers, negative numbers, and zero.
- Addition: The process of calculating the total of two or more numbers or amounts.
- Subtraction: Subtraction is a process of finding out the difference between two numbers, by reducing one number from another.
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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.
