189 LearnersLast updated on May 26th, 2025
Divisibility Rule of 213
The divisibility rule is a way to determine whether a number is divisible by another number without using the division method. In real life, we can use divisibility rules for quick math, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 213.
What is the Divisibility Rule of 213?
The divisibility rule for 213 is a method by which we can determine if a number is divisible by 213 without using the division method. Check whether 639 is divisible by 213 using the divisibility rule.
Step 1: Triple the last digit of the number, here in 639, 9 is the last digit, so triple it. 9 × 3 = 27.
Step 2: Add the result from Step 1 to the remaining digits of the number (excluding the last digit). i.e., 63 + 27 = 90.
Step 3: As it is shown that 90 is not a multiple of 213, the number is not divisible by 213. If the result from Step 2 is a multiple of 213, then the number is divisible by 213.
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Tips and Tricks for Divisibility Rule of 213
Learning the divisibility rule will help kids master division. Let’s explore some tips and tricks for the divisibility rule of 213.
Know the multiples of 213:
Memorize the multiples of 213 (213, 426, 639, 852, etc.) to quickly check divisibility. If the result from the addition is a multiple of 213, then the number is divisible by 213.
Use the negative numbers:
If the result we get after the addition is negative, we will ignore 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 213. For example, check if 852 is divisible by 213 using the divisibility test. Triple the last digit by 3, i.e., 2 × 3 = 6. Add this to the remaining digits excluding the last digit, 85 + 6 = 91. Since 91 is not a multiple of 213, 852 is not divisible by 213.
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 verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 213
The divisibility rule of 213 helps us quickly check if a given number is divisible by 213, but common mistakes like calculation errors can lead to incorrect conclusions. Here, we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which are to triple the last digit and then add the result to the remaining digits, excluding the last digit, and check whether it is a multiple of 213.
Mistake 2
Including the last digit in addition.
Students should keep in mind that they should exclude the last digit while adding 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 as a result of the addition. The process should be repeated until we get the smallest number that is divisible by 213.
Mistake 4
Not considering negative values.
Students might consider negative values as invalid for divisibility rules. But the divisibility rule is applicable to negative values too. So, students should consider negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps.
Students often confuse the steps or forget them. To avoid errors, students should practice regularly.
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Divisibility Rule of 213 Examples
Problem 1
Is 2130 divisible by 213?
Yes, 2130 is divisible by 213.
Explanation
To check if 2130 is divisible by 213, we can perform a simple division.
1) Divide 2130 by 213, which gives 2130 ÷ 213 = 10.
2) Since the result is an integer, 2130 is divisible by 213.
Problem 2
Check the divisibility rule of 213 for 426
Yes, 426 is divisible by 213.
Explanation
To check if 426 is divisible by 213:
1) Divide 426 by 213, which gives 426 ÷ 213 = 2.
2) Since the result is an integer, 426 is divisible by 213.
Problem 3
Is 639 divisible by 213?
Yes, 639 is divisible by 213.
Explanation
To verify divisibility of 639 by 213:
1) Divide 639 by 213, which gives 639 ÷ 213 = 3.
2) Since the result is an integer, 639 is divisible by 213.
Problem 4
Can 321 be divisible by 213 following the divisibility rule?
No, 321 is not divisible by 213.
Explanation
To determine if 321 is divisible by 213:
1) Divide 321 by 213, which gives 321 ÷ 213 ≈ 1.507.
2) Since the result is not an integer, 321 is not divisible by 213.
Problem 5
Check the divisibility rule of 213 for 852.
Yes, 852 is divisible by 213.
Explanation
To check if 852 is divisible by 213:
1) Divide 852 by 213, which gives 852 ÷ 213 = 4.
2) Since the result is an integer, 852 is divisible by 213.
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FAQs on Divisibility Rule of 213
1.What is the divisibility rule for 213?
2.How many numbers are there between 1 and 1000 that are divisible by 213?
3. Is 426 divisible by 213?
4.What if I get 0 after adding?
5. Does the divisibility rule of 213 apply to all integers?
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Important Glossaries for Divisibility Rule of 213
- Divisibility rule: A 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 the number ends in an even number.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 213 are 213, 426, 639, 852, etc.
- Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
- Addition: Addition is the process of finding the total or sum by combining two numbers or more.
- Verification: Verification is the process of confirming the correctness of a result by cross-checking through a different method, such as the division method.
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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.
