192 LearnersLast updated on May 26th, 2025
Divisibility Rule of 69
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 69.
What is the Divisibility Rule of 69?
The divisibility rule for 69 is a method by which we can find out if a number is divisible by 69 or not without using the division method. Check whether 4140 is divisible by 69 with the divisibility rule.
Step 1: Check if the number is divisible by both 3 and 23, as 69 is the product of these two prime numbers.
Step 2: For divisibility by 3, add the digits of the number and check if the sum is divisible by 3. For 4140, 4+1+4+0=9, which is divisible by 3.
Step 3: For divisibility by 23, use the division method or another rule specific to 23, as there is no simple rule for it.
Step 4: Since 4140 is divisible by both 3 and 23, it is divisible by 69.
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Tips and Tricks for Divisibility Rule of 69
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 69.
- Know the factors: Memorize the factors of 69, which are 3 and 23, to quickly check divisibility. If a number is divisible by both 3 and 23, then it is divisible by 69.
- Use addition for 3: For divisibility by 3, add all the digits of the number and check if the result is divisible by 3.
- Repeat the process for large numbers: Students should keep repeating the divisibility process for both 3 and 23 until they reach a conclusion about divisibility by 69.
- 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 learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 69
The divisibility rule of 69 helps us quickly check if a given number is divisible by 69, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking divisibility for both factors.
Ensure you check divisibility by both 3 and 23, as 69 is the product of these two numbers.
Mistake 2
Incorrectly adding digits for divisibility by 3.
Carefully add the digits of the number and check if the sum is divisible by 3.
Mistake 3
Not using a method for divisibility by 23.
Use the division method or another rule specific to checking divisibility by 23.
Mistake 4
Confusing the steps.
Students often confuse the steps or forget them. To avoid this error, students should practice regularly.
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Divisibility Rule of 69 Examples
Problem 1
Can 345 be divisible by 69?
No, 345 is not divisible by 69.
Explanation
To check if 345 is divisible by 69, we'll use a unique approach:
1) Double the last digit and add it to the rest of the number: 5 × 2 = 10, 34 + 10 = 44.
2) Check if 44 is divisible by 69. No, 44 is not divisible by 69.
Problem 2
Is 828 divisible by 69?
Yes, 828 is divisible by 69.
Explanation
To check if 828 is divisible by 69, follow these steps:
1) Double the last digit and add it to the rest of the number: 8 × 2 = 16, 82 + 16 = 98.
2) Check if 98 is a multiple of 69. No, it's not. However, 828 is divisible by 69 (69 × 12 = 828), confirming the divisibility.
Problem 3
Check the divisibility rule of 69 for 1380.
Yes, -207 is divisible by 69.
Explanation
To check if -207 is divisible by 69, disregard the negative sign and proceed:
1) Double the last digit and add it to the rest of the number: 7 × 2 = 14, 20 + 14 = 34.
2) Check if 34 is a multiple of 69. No, but -207 is divisible by 69 (-69 × 3 = -207), hence confirming the divisibility.
Problem 4
Is -207 divisible by 69?
Yes, -207 is divisible by 69.
Explanation
To check if -207 is divisible by 69, disregard the negative sign and proceed:
1) Double the last digit and add it to the rest of the number: 7 × 2 = 14, 20 + 14 = 34.
2) Check if 34 is a multiple of 69. No, but -207 is divisible by 69 (-69 × 3 = -207), hence confirming the divisibility.
Problem 5
Verify if 276 is divisible by 69.
Yes, 276 is divisible by 69.
Explanation
To check if 276 is divisible by 69:
1) Double the last digit and add it to the rest of the number: 6 × 2 = 12, 27 + 12 = 39.
2) Check if 39 is a multiple of 69. No, but 276 is divisible by 69 (69 × 4 = 276), confirming the divisibility.
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FAQs on Divisibility Rule of 69
1.What is the divisibility rule for 69?
2. How many numbers are there between 1 and 100 that are divisible by 69?
3. Is 138 divisible by 69?
4. What if I get 0 after checking divisibility by a factor?
5.Does the divisibility rule of 69 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 69?
7.What are some fun ways kids in India can practice Divisibility Rule of 69 with numbers?
8.What role do numbers and Divisibility Rule of 69 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Divisibility Rule of 69 skills?
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Important Glossaries for Divisibility Rule of 69
- Divisibility Rule: A set of rules used to determine whether a number is divisible by another number without performing the actual division.
- Factors: Numbers that can multiply together to get another number. For example, the factors of 69 are 3 and 23.
- Multiples: Results obtained after multiplying a number by an integer. For example, multiples of 69 are 69, 138, 207, etc.
- Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself. For example, 3 and 23 are prime numbers.
- Division Method: A mathematical procedure used to determine how many times one number is contained within another.
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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.
