190 LearnersLast updated on May 26th, 2025
Divisibility Rule of 63
The divisibility rule is a method to determine if a number is divisible by another number without performing actual division. In real life, this can be used for quick calculations, evenly dividing items, and sorting. In this topic, we will explore the divisibility rule of 63.
What is the Divisibility Rule of 63?
The divisibility rule for 63 allows us to determine if a number is divisible by 63 without using division. Check whether 756 is divisible by 63 using the divisibility rule.
Step 1: Check if the number is divisible by both 7 and 9, as 63 is the product of these two numbers.
Step 2: To check divisibility by 7, multiply the last digit by 2 and subtract it from the rest of the number. For 756, multiply 6 by 2 to get 12 and subtract from 75 to get 63, which is divisible by 7.
Step 3: To check divisibility by 9, add all the digits of the number. For 756, the sum is 7 + 5 + 6 = 18, which is divisible by 9.
Since 756 is divisible by both 7 and 9, it is divisible by 63.
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Tips and Tricks for Divisibility Rule of 63
Understanding divisibility rules will help improve division skills. Here are some tips and tricks for the divisibility rule of 63:
Know the multiples of 63:
Memorize multiples of 63 (63, 126, 189, 252, etc.) to quickly verify divisibility.
Use negative numbers:
If after subtraction the result is negative, consider it as positive to check divisibility.
Repeat the process for large numbers:
If the number is large, repeat the divisibility check for both 7 and 9 until reaching a smaller number.
Use the division method to verify:
Use the division method to confirm and crosscheck results for better understanding.
Common Mistakes and How to Avoid Them in Divisibility Rule of 63
The divisibility rule of 63 helps quickly determine divisibility, but mistakes in calculations can lead to errors. Here are some common mistakes and solutions:
Mistake 1
Forgetting to check both criteria.
Remember to check divisibility by both 7 and 9.
Mistake 2
Including the last digit in subtraction incorrectly.
Exclude the last digit when subtracting for the divisibility rule of 7.
Mistake 3
Stopping the process prematurely.
Continue the process until achieving a definitive result.
Mistake 4
Ignoring negative results.
Treat negative results as positive for divisibility checks.
Mistake 5
Confusing the steps.
Practice regularly to memorize the correct steps.
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Divisibility Rule of 63 Examples
Problem 1
Is 756 divisible by 63?
Yes, 756 is divisible by 63.
Explanation
To check divisibility by 63, we need to ensure divisibility by both 7 and 9, since 63 = 7 × 9.
1) Check divisibility by 7: Multiply the last digit by 2, 6 × 2 = 12. Subtract from the rest, 75 – 12 = 63, which is divisible by 7.
2) Check divisibility by 9: Add all digits, 7 + 5 + 6 = 18, which is divisible by 9.
Since 756 is divisible by both 7 and 9, it is divisible by 63.
Problem 2
Can 945 be divisible by 63 following the divisibility rule?
Can 945 be divisible by 63 following the divisibility rule?
Explanation
Check divisibility by both 7 and 9.
1) For 7: Multiply the last digit by 2, 5 × 2 = 10. Subtract from the rest, 94 – 10 = 84, which is divisible by 7.
2) For 9: Add the digits, 9 + 4 + 5 = 18, which is divisible by 9.
945 is divisible by both 7 and 9, so it is divisible by 63.
Problem 3
Is 378 divisible by 63?
Yes, 378 is divisible by 63.
Explanation
Check divisibility by both 7 and 9.
1) For 7: Multiply the last digit by 2, 8 × 2 = 16. Subtract from the rest, 37 – 16 = 21, which is divisible by 7.
2) For 9: Add the digits, 3 + 7 + 8 = 18, which is divisible by 9.
Since 378 is divisible by both 7 and 9, it is divisible by 63.
Problem 4
Is 512 divisible by 63?
No, 512 is not divisible by 63.
Explanation
Check divisibility by both 7 and 9.
1) For 7: Multiply the last digit by 2, 2 × 2 = 4. Subtract from the rest, 51 – 4 = 47, which is not divisible by 7.
2) For 9: Add the digits, 5 + 1 + 2 = 8, which is not divisible by 9.
512 is neither divisible by 7 nor 9, so it is not divisible by 63.
Problem 5
Check the divisibility rule of 63 for 1260.
Yes, 1260 is divisible by 63.
Explanation
Check divisibility by both 7 and 9.
1) For 7: Multiply the last digit by 2, 0 × 2 = 0. Subtract from the rest, 126 – 0 = 126. Repeat the process: 6 × 2 = 12, 12 – 12 = 0, which is divisible by 7.
2) For 9: Add the digits, 1 + 2 + 6 + 0 = 9, which is divisible by 9.
Since 1260 is divisible by both 7 and 9, it is divisible by 63.
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FAQs on Divisibility Rule of 63
1.What is the divisibility rule for 63?
2.How many numbers between 1 and 200 are divisible by 63?
3.Is 189 divisible by 63?
4.What if I get 0 after subtracting for the rule of 7?
5.Does the divisibility rule of 63 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 63?
7.What are some fun ways kids in United States can practice Divisibility Rule of 63 with numbers?
8.What role do numbers and Divisibility Rule of 63 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 63 skills?
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Important Glossaries for Divisibility Rule of 63
- Divisibility rule: A set of guidelines to determine if a number is divisible by another without performing division.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 63 are 63, 126, 189, etc.
- Integers: Numbers including whole numbers, negative numbers, and zero.
- Subtraction: The process of finding the difference between two numbers by reducing one from another.
- Product: The result of multiplying two numbers. For example, the product of 7 and 9 is 63.
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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.
