189 LearnersLast updated on May 26th, 2025
Divisibility Rule of 219
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 219.
What is the Divisibility Rule of 219?
The divisibility rule for 219 is a method by which we can find out if a number is divisible by 219 or not without using the division method. Check whether 438 is divisible by 219 with the divisibility rule.
Step 1: Multiply the last digit of the number by 20, here in 438, 8 is the last digit, multiply it by 20. 8 × 20 = 160
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit, i.e., 43–160 = -117.
Step 3: As it is shown that -117 is not a multiple of 219, therefore, the number is not divisible by 219. If the result from step 2 is a multiple of 219, then the number is divisible by 219.
Tips and Tricks for Divisibility Rule of 219
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 219.
Know the multiples of 219:
Memorize the multiples of 219 (219, 438, 657, 876, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 219, then the number is divisible by 219.
Use the 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 219.
For example: Check if 657 is divisible by 219 using the divisibility test. Multiply the last digit by 20, i.e., 7 × 20 = 140. Subtract the remaining digits excluding the last digit by 140, 65–140 = -75. Still, -75 is not a multiple of 219, hence 657 is not divisible by 219.
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 219
The divisibility rule of 219 helps us to quickly check if the given number is divisible by 219, 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 are multiplying the last digit with 20 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 219.
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 got a large number to result in after subtraction. The process should be repeated until we get the smallest number that is divisible by 219.
Mistake 4
Not considering the negative values.
Students consider the 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 the steps. To avoid the error, students should practice regularly.
Divisibility Rule of 219 Examples
Problem 1
Is 657 divisible by 219?
Yes, 657 is divisible by 219.
Explanation
To verify if 657 is divisible by 219, we can use the divisibility rule for 219.
1) Break down the number 657 into three parts: hundreds, tens, and units.
2) Multiply the hundreds digit (6) by 2, the tens digit (5) by 3, and the units digit (7) by 1.
3) Calculate the sum: (6 x 2) + (5 x 3) + (7 x 1) = 12 + 15 + 7 = 34.
4) Since 34 is not a multiple of 219, the process doesn't confirm divisibility by 219. However, performing direct division shows 657 ÷ 219 = 3 without a remainder, confirming that 657 is indeed divisible by 219.
Problem 2
Check the divisibility rule of 219 for 876.
No, 876 is not divisible by 219.
Explanation
To determine divisibility by 219, follow these steps:
1) Consider each digit, multiplying the hundreds digit (8) by 2, the tens digit (7) by 3, and the units digit (6) by 1.
2) Add these values together: (8 x 2) + (7 x 3) + (6 x 1) = 16 + 21 + 6 = 43.
3) Check if 43 is a multiple of 219. Since it is not, 876 is not divisible by 219.
Problem 3
Is -438 divisible by 219?
Yes, -438 is divisible by 219.
Explanation
To determine divisibility for a negative number like -438:
1) Ignore the negative sign and consider 438.
2) Multiply the hundreds digit (4) by 2, the tens digit (3) by 3, and the units digit (8) by 1.
3) Add them up: (4 x 2) + (3 x 3) + (8 x 1) = 8 + 9 + 8 = 25.
4) Since 25 is not a multiple of 219, we check directly: 438 ÷ 219 = 2, without a remainder, confirming -438 is divisible by 219.
Problem 4
Can 342 be divisible by 219 following the divisibility rule?
No, 342 is not divisible by 219.
Explanation
To verify if 342 is divisible by 219:
1) Multiply the hundreds digit (3) by 2, the tens digit (4) by 3, and the units digit (2) by 1.
2) Add these results: (3 x 2) + (4 x 3) + (2 x 1) = 6 + 12 + 2 = 20.
3) Since 20 is not a multiple of 219, 342 is not divisible by 219.
Problem 5
Check the divisibility rule of 219 for 1095.
Yes, 1095 is divisible by 219.
Explanation
To check if 1095 is divisible by 219, follow the steps:
1) Multiply the thousands digit (1) by 2, the hundreds digit (0) by 3, the tens digit (9) by 1, and the units digit (5) by 1.
2) Calculate the sum: (1 x 2) + (0 x 3) + (9 x 1) + (5 x 1) = 2 + 0 + 9 + 5 = 16.
3) Since 16 is not a multiple of 219, direct division shows 1095 ÷ 219 = 5 without a remainder, confirming divisibility by 219.
FAQs on Divisibility Rule of 219
1. What is the divisibility rule for 219?
2. How many numbers are there between 1 and 1000 that are divisible by 219?
3.Is 876 divisible by 219?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 219 apply to all the integers?
6.How can children in Singapore use numbers in everyday life to understand Divisibility Rule of 219?
7.What are some fun ways kids in Singapore can practice Divisibility Rule of 219 with numbers?
8.What role do numbers and Divisibility Rule of 219 play in helping children in Singapore develop problem-solving skills?
9.How can families in Singapore create number-rich environments to improve Divisibility Rule of 219 skills?
Important Glossaries for Divisibility Rule of 219
- 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 219 if the process described results in a multiple of 219.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 219 are 219, 438, 657, 876, 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.
- Verify: To confirm the accuracy of a mathematical process or result, often by using an alternative method such as division.
Explore More numbers
About BrightChamps in Singapore
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.
