152 LearnersLast updated on May 26th, 2025
Divisibility Rule of 693
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 693.
What is the Divisibility Rule of 693?
The divisibility rule for 693 is a method by which we can find out if a number is divisible by 693 or not without using the division method. Check whether 1386 is divisible by 693 using the divisibility rule.
Step 1: Break down 693 into its prime factors: 693 = 3 × 3 × 7 × 11.
Step 2: Check if the number is divisible by each of these factors.
To check divisibility by 3, ensure the sum of the digits is divisible by 3.
For 1386, 1 + 3 + 8 + 6 = 18, which is divisible by 3.
To check divisibility by 7, follow the specific rule for 7 (as described earlier).
For 1386, double the last digit (6): 6 × 2 = 12. Subtract from the remaining number: 138 - 12 = 126. Since 126 is divisible by 7, 1386 passes this test.
To check divisibility by 11, see if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is a multiple of 11.
For 1386, (1 + 8) - (3 + 6) = 9 - 9 = 0, which is a multiple of 11.
Since 1386 is divisible by 3, 7, and 11, it is divisible by 693.
Tips and Tricks for Divisibility Rule of 693
- Know the prime factors: Memorize the prime factors of 693 (3, 7, and 11) to quickly check divisibility.
- Use the divisibility rules for each factor: Familiarize yourself with the divisibility rules for 3, 7, and 11, as these will help you determine if a number is divisible by 693.
- Verify by division: Once you determine divisibility by 3, 7, and 11, you can verify your result by dividing the original number by 693 to ensure no remainder.
- Practice: Regular practice with different numbers will help you become proficient in applying the divisibility rule for 693.
- Simplify large numbers: Break down large numbers into smaller parts to check divisibility more easily.
Common Mistakes and How to Avoid Them in Divisibility Rule of 693
The divisibility rule of 693 involves checking divisibility by multiple factors, which can lead to common mistakes. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Ignoring one of the factors.
Always remember to check divisibility by all three factors: 3, 7, and 11.
Mistake 2
Misapplying divisibility rules.
Ensure you correctly apply the divisibility rules for 3, 7, and 11.
Mistake 3
Not verifying with division.
Use the division method to cross-check your results and ensure accuracy.
Mistake 4
Skipping steps due to large numbers.
Break down large numbers into smaller components and apply the divisibility rules step by step.
Mistake 5
Confusing the steps.
Practice consistently to remember the steps and apply them correctly.
Divisibility Rule of 693 Examples
Problem 1
Is 2079 divisible by 693?
Yes, 2079 is divisible by 693.
Explanation
To determine if 2079 is divisible by 693, follow these steps:
1) Divide 2079 by 693.
2) The result is exactly 3, with no remainder, indicating that 2079 is divisible by 693.
Problem 2
Check the divisibility rule of 693 for 1386.
Yes, 1386 is divisible by 693.
Explanation
To verify if 1386 is divisible by 693:
1) Divide 1386 by 693.
2) The quotient is 2, with zero remainder, confirming that 1386 is divisible by 693.
Problem 3
Is -693 divisible by 693?
Yes, -693 is divisible by 693.
Explanation
To check the divisibility of -693 by 693:
1) Remove the negative sign and divide 693 by 693.
2) The result is 1, with no remainder, so -693 is divisible by 693.
Problem 4
Can 500 be divisible by 693 following the divisibility rule?
No, 500 isn't divisible by 693.
Explanation
To determine if 500 is divisible by 693:
1) Divide 500 by 693.
2) The result is a fraction, indicating that 500 is not divisible by 693.
Problem 5
Check the divisibility rule of 693 for 3465.
Yes, 3465 is divisible by 693.
Explanation
To check if 3465 is divisible by 693:
1) Divide 3465 by 693.
2) The result is 5, with no remainder, confirming that 3465 is divisible by 693.
FAQs on Divisibility Rule of 693
1.What is the divisibility rule for 693?
2.How can you quickly check divisibility by 693?
3.Is 2079 divisible by 693?
4.What if I get a remainder when dividing?
5.Does the divisibility rule of 693 apply to all integers?
6.How can children in United Kingdom use numbers in everyday life to understand Divisibility Rule of 693?
7.What are some fun ways kids in United Kingdom can practice Divisibility Rule of 693 with numbers?
8.What role do numbers and Divisibility Rule of 693 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Divisibility Rule of 693 skills?
Important Glossaries for Divisibility Rule of 693
- Divisibility Rule: The set of rules used to determine if a number is divisible by another without direct division.
- Prime Factors: The prime numbers that multiply together to give the original number. For 693, these are 3, 7, and 11.
- Multiples: Numbers obtained by multiplying a number by integers. For example, multiples of 693 include 693, 1386, etc.
- Sum of Digits: The total when adding all digits of a number, used to check divisibility by 3.
- Alternating Sum: The difference between the sum of digits in odd positions and even positions, used for checking divisibility by 11.
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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.
