197 LearnersLast updated on May 26th, 2025
Divisibility Rule of 21
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 21.
What is the Divisibility Rule of 21?
The divisibility rule for 21 is a method by which we can find out if a number is divisible by 21 without using the division method. Check whether 462 is divisible by 21 with the divisibility rule.
Step 1: Check if the number is divisible by 3. Add up all the digits in the number and see if the sum is divisible by 3. For 462, the sum of digits is 4+6+2=12, which is divisible by 3.
Step 2: Check if the number is divisible by 7. Use the divisibility rule of 7: double the last digit and subtract it from the rest of the number. For 462, double the last digit: 2×2=4. Subtract from the rest: 46-4=42, which is divisible by 7.
Step 3: Since the number is divisible by both 3 and 7, it is divisible by 21.
Tips and Tricks for Divisibility Rule of 21
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 21.
- Know the multiples of 21: Memorize the multiples of 21 (21, 42, 63, 84… etc.) to quickly check divisibility. If the result from any divisibility test is a multiple of 21, then the number is divisible by 21.
- Use the divisibility rules for both 3 and 7: A number must satisfy both the rule for 3 and the rule for 7 to be divisible by 21.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that can be easily evaluated. For example, check if 882 is divisible by 21 using the divisibility test.
For 3: The sum of digits is 8+8+2=18, which is divisible by 3.
For 7: Double the last digit, 2×2=4. Subtract from the rest, 88 - 4 = 84, which is divisible by 7.
Hence, 882 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 21
The divisibility rule of 21 helps us to quickly check if the given number is divisible by 21, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following both divisibility rules.
Ensure that the number satisfies both the divisibility rules for 3 and 7.
Divisibility Rule of 21 Examples
Problem 1
Is 189 divisible by 21?
Yes, 189 is divisible by 21.
Explanation
To determine if 189 is divisible by 21, we can apply the divisibility rules for both 3 and 7.
1) Check divisibility by 3: Add the digits, 1 + 8 + 9 = 18. Since 18 is divisible by 3, 189 passes this test.
2) Check divisibility by 7: Multiply the last digit by 2, 9 × 2 = 18. Subtract from the remaining digits, 18 - 18 = 0. Since 0 is a multiple of 7, 189 also passes this test.
Since 189 is divisible by both 3 and 7, it is divisible by 21.
Problem 2
Check the divisibility rule of 21 for 252.
Yes, 252 is divisible by 21.
Explanation
To check if 252 is divisible by 21, we use the divisibility rules for 3 and 7.
1) Divisibility by 3: Add the digits, 2 + 5 + 2 = 9. Since 9 is divisible by 3, 252 passes this test.
2) Divisibility by 7: Multiply the last digit by 2, 2 × 2 = 4. Subtract from the remaining digits, 25 - 4 = 21. Since 21 is a multiple of 7, 252 passes this test.
Therefore, 252 is divisible by 21.
Problem 3
Is 63 divisible by 21?
Yes, 63 is divisible by 21.
Explanation
To verify if 63 is divisible by 21, we need to check its divisibility by both 3 and 7.
1) Divisibility by 3: Add the digits, 6 + 3 = 9. Since 9 is divisible by 3, 63 passes this test.
2) Divisibility by 7: Multiply the last digit by 2, 3 × 2 = 6. Subtract from the remaining digits, 6 - 6 = 0. Since 0 is a multiple of 7, 63 passes this test.
Thus, 63 is divisible by 21.
Problem 4
Can 154 be divisible by 21 following the divisibility rule?
No, 154 is not divisible by 21.
Explanation
To check if 154 is divisible by 21, apply the divisibility rules for 3 and 7.
1) Divisibility by 3: Add the digits, 1 + 5 + 4 = 10. Since 10 is not divisible by 3, 154 fails this test.
2) Divisibility by 7: Multiply the last digit by 2, 4 × 2 = 8. Subtract from the remaining digits, 15 - 8 = 7. Since 7 is a multiple of 7, 154 passes this test.
Since 154 is not divisible by 3, it is not divisible by 21.
Problem 5
Check the divisibility rule of 21 for 441.
Yes, 441 is divisible by 21.
Explanation
To determine if 441 is divisible by 21, we use the divisibility rules for 3 and 7.
1) Divisibility by 3: Add the digits, 4 + 4 + 1 = 9. Since 9 is divisible by 3, 441 passes this test.
2) Divisibility by 7: Multiply the last digit by 2, 1 × 2 = 2. Subtract from the remaining digits, 44 - 2 = 42. Since 42 is a multiple of 7, 441 passes this test.
Therefore, 441 is divisible by 21.
FAQs on Divisibility Rule of 21
1.What is the divisibility rule for 21?
2.How many numbers are there between 1 and 100 that are divisible by 21?
3.Is 63 divisible by 21?
4.What if I get 0 after using the divisibility rule of 7?
5.Does the divisibility rule of 21 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 21?
7.What are some fun ways kids in United States can practice Divisibility Rule of 21 with numbers?
8.What role do numbers and Divisibility Rule of 21 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 21 skills?
Important Glossaries for Divisibility Rule of 21
- Divisibility Rule: A set of guidelines used to determine whether a number is divisible by another number without performing division.
- Multiples: The result of multiplying a number by an integer. For example, multiples of 21 are 21, 42, 63, etc.
- Integers: The set of whole numbers and their opposites, including positive numbers, negative numbers, and zero.
- Subtraction: A mathematical operation that involves removing one number from another to find the difference.
- Sum: The result of adding two or more numbers together.
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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
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