190 LearnersLast updated on May 26th, 2025
Divisibility Rule of 109
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 109.
What is the Divisibility Rule of 109?
The divisibility rule for 109 is a method by which we can find out if a number is divisible by 109 or not without using the division method. Check whether 2180 is divisible by 109 with the divisibility rule.
Step 1: Take the last two digits of the number. Here in 2180, 80 is the last two digits. Multiply the last two digits by 9. 80 × 9 = 720.
Step 2: Subtract the result from Step 1 from the remaining part of the number. i.e., 21 - 720 = -699.
Step 3: Since -699 is not a multiple of 109, 2180 is not divisible by 109. If the result from step 2 is a multiple of 109, then the number is divisible by 109.
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Tips and Tricks for Divisibility Rule of 109
Learning the divisibility rule will help individuals master division. Let’s learn a few tips and tricks for the divisibility rule of 109.
Know the multiples of 109:
Memorize the multiples of 109 (109, 218, 327, 436, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 109, then the number is divisible by 109.
Handle negative numbers appropriately:
If the result after the subtraction is negative, we should consider the absolute value for checking the divisibility of a number.
Repeat the process for large numbers:
Individuals should keep repeating the divisibility process until they reach a small number that is divisible by 109. For example, check if 3279 is divisible by 109 using the divisibility test. Take the last two digits, 79, multiply by 9, i.e., 79 × 9 = 711. Subtract 711 from the remaining number excluding the last two digits, 32 - 711 = -679. Since -679 is not a multiple of 109, 3279 is not divisible by 109.
Use the division method to verify:
Individuals can use the division method as a way to verify and cross-check their results. This will help them verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 109
The divisibility rule of 109 helps us to quickly check if the given number is divisible by 109, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you avoid them.
Mistake 1
Not following the correct steps.
Follow the correct steps, which involve multiplying the last two digits by 9 and then subtracting the result from the remaining digits of the number.
Mistake 2
Including the last two digits in subtraction.
Exclude the last two digits while subtracting and include only the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Repeat the process until a small number that is divisible by 109 is obtained.
Mistake 4
Not considering the absolute value of negative results.
Consider the absolute value (positive value) when checking for divisibility.
Mistake 5
Confusing the steps
Practice regularly to become familiar with the steps and avoid confusion.
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Divisibility Rule of 109 Examples
Problem 1
Can 2180 be divisible by 109?
Yes, 2180 is divisible by 109.
Explanation
To determine if 2180 is divisible by 109, we use the divisibility rule:
1) Double the last digit of the number, 0 × 2 = 0.
2) Subtract the result from the remaining digits, 218 - 0 = 218.
3) Check if 218 is divisible by 109. Yes, 218 is a multiple of 109 (109 × 2 = 218).
Problem 2
Is 6545 divisible by 109?
Yes, 6545 is divisible by 109.
Explanation
To verify the divisibility of 6545 by 109:
1) Double the last digit, 5 × 2 = 10.
2) Subtract this result from the remaining digits, 654 - 10 = 644.
3) Check if 644 is divisible by 109. Yes, 644 is a multiple of 109 (109 × 5 = 545).
Problem 3
Determine if -327 is divisible by 109.
No, -327 is not divisible by 109.
Explanation
To check divisibility of -327 by 109:
1) Ignore the negative sign and focus on 327.
2) Double the last digit, 7 × 2 = 14.
3) Subtract this from the remaining digits, 32 - 14 = 18.
4) Check if 18 is a multiple of 109. No, 18 is not a multiple of 109.
Problem 4
Is 763 divisible by 109?
No, 763 is not divisible by 109.
Explanation
To determine divisibility of 763 by 109:
1) Double the last digit, 3 × 2 = 6.
2) Subtract this from the remaining digits, 76 - 6 = 70.
3) Check if 70 is a multiple of 109. No, 70 is not a multiple of 109.
Problem 5
Check if 1199 is divisible by 109.
Yes, 1199 is divisible by 109.
Explanation
To confirm divisibility of 1199 by 109:
1) Double the last digit, 9 × 2 = 18.
2) Subtract this from the remaining digits, 119 - 18 = 101.
3) Check if 101 is a multiple of 109. Yes, 101 is a multiple of 109 (109 × 11 = 1199).
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FAQs on Divisibility Rule of 109
1.What is the divisibility rule for 109?
2.How many numbers are there between 1 and 1000 that are divisible by 109?
3.Is 327 divisible by 109?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 109 apply to all integers?
6.How can children in Australia use numbers in everyday life to understand Divisibility Rule of 109?
7.What are some fun ways kids in Australia can practice Divisibility Rule of 109 with numbers?
8.What role do numbers and Divisibility Rule of 109 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Divisibility Rule of 109 skills?
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Important Glossary for Divisibility Rule of 109
- 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 2 if it ends with an even digit.
- Multiples: Multiples are the results obtained after multiplying a number by an integer. For example, multiples of 109 are 109, 218, 327, etc.
- Integers: Integers 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.
- Absolute value: The non-negative value of a number without regard to its sign. For example, the absolute value of -5 is 5.
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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.
