123 LearnersLast updated on May 26th, 2025
Divisibility Rule of 65
The divisibility rule is a method to determine 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 65.
What is the Divisibility Rule of 65?
The divisibility rule for 65 is a method by which we can find out if a number is divisible by 65 without using the division method. Check whether 8450 is divisible by 65 with the divisibility rule.
Step 1: A number is divisible by 65 if it is divisible by both 5 and 13.
Step 2: To check divisibility by 5, the last digit of the number should be 0 or 5. Since 8450 ends with 0, it is divisible by 5.
Step 3: To check divisibility by 13, add 4 times the last digit to the rest of the number, and see if the result is divisible by 13. For 8450, multiply the last digit 0 by 4: 0 × 4 = 0. Add this to 845: 845 + 0 = 845.
Step 4: Repeat the process for 845. Multiply the last digit 5 by 4: 5 × 4 = 20. Add this to 84: 84 + 20 = 104.
Step 5: Since 104 is a multiple of 13, the original number 8450 is divisible by 13.
Conclusion: Since 8450 is divisible by both 5 and 13, it is divisible by 65.
Tips and Tricks for Divisibility Rule of 65
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 65.
Know the multiples of 65:
Memorize the multiples of 65 (65, 130, 195, 260, etc.) to quickly check the divisibility. If the result from the process is a multiple of 65, then the number is divisible by 65.
Use the negative numbers:
If the result we get after the process is negative, we can consider its absolute value 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 65.
For example: Check if 8450 is divisible by 65 using the divisibility test.
Follow the steps as explained above.
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 65
The divisibility rule of 65 helps us quickly check if a given number is divisible by 65, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps: check divisibility by 5 (last digit 0 or 5) and then check divisibility by 13 using the process provided.
Divisibility Rule of 65 Examples
Problem 1
Can 845 be considered divisible by 65?
No, 845 is not divisible by 65.
Explanation
To check if 845 is divisible by 65, we need to verify divisibility by both 5 and 13 (since 65 = 5 × 13).
1) For divisibility by 5, the last digit should be 0 or 5. In 845, the last digit is 5, so it is divisible by 5.
2) Now, check divisibility by 13. Add 4 times the last digit to the rest of the number: 4 × 5 = 20, then 84 + 20 = 104.
3) Check if 104 is divisible by 13. 104 ÷ 13 = 8, so it is divisible by 13.
Since 845 is divisible by both 5 and 13, it is divisible by 65.
Problem 2
Is 1300 divisible by 65?
Yes, 1300 is divisible by 65.
Explanation
To determine if 1300 is divisible by 65, check divisibility by both 5 and 13.
1) For divisibility by 5, the last digit should be 0 or 5. The last digit in 1300 is 0, so it is divisible by 5.
2) For divisibility by 13, add 4 times the last digit to the rest of the number: 4 × 0 = 0, then 130 + 0 = 130.
3) Check if 130 is divisible by 13. 130 ÷ 13 = 10, so it is divisible by 13.
Since 1300 is divisible by both 5 and 13, it is divisible by 65.
Problem 3
Apply the divisibility rule of 65 to 780.
Yes, 780 is divisible by 65.
Explanation
To verify if 780 is divisible by 65, we need to check if it is divisible by both 5 and 13.
1) For divisibility by 5, the last digit should be 0 or 5. The last digit in 780 is 0, so it is divisible by 5.
2) For divisibility by 13, add 4 times the last digit to the rest of the number: 4 × 0 = 0, then 78 + 0 = 78.
3) Check if 78 is divisible by 13. 78 ÷ 13 = 6, so it is divisible by 13.
Since 780 is divisible by both 5 and 13, it is divisible by 65.
Problem 4
Determine if 455 is divisible by 65.
No, 455 is not divisible by 65.
Explanation
To check if 455 is divisible by 65, we need to check divisibility by both 5 and 13.
1) For divisibility by 5, the last digit should be 0 or 5. The last digit in 455 is 5, so it is divisible by 5.
2) For divisibility by 13, add 4 times the last digit to the rest of the number: 4 × 5 = 20, then 45 + 20 = 65.
3) Check if 65 is divisible by 13. 65 ÷ 13 = 5, so it is divisible by 13.
Since 455 is divisible by both 5 and 13, it is divisible by 65.
Problem 5
Check the divisibility of 520 by 65.
Yes, 520 is divisible by 65.
Explanation
To verify if 520 is divisible by 65, check divisibility by both 5 and 13.
1) For divisibility by 5, the last digit should be 0 or 5. The last digit in 520 is 0, so it is divisible by 5.
2) For divisibility by 13, add 4 times the last digit to the rest of the number: 4 × 0 = 0, then 52 + 0 = 52.
3) Check if 52 is divisible by 13. 52 ÷ 13 = 4, so it is divisible by 13.
Since 520 is divisible by both 5 and 13, it is divisible by 65.
FAQs on Divisibility Rule of 65
1.What is the divisibility rule for 65?
2.How many numbers are there between 1 and 1000 that are divisible by 65?
3.Is 390 divisible by 65?
4.What if I get 0 after the process?
5.Does the divisibility rule of 65 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 65?
7.What are some fun ways kids in India can practice Divisibility Rule of 65 with numbers?
8.What role do numbers and Divisibility Rule of 65 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 65 skills?
Important Glossaries for Divisibility Rule of 65
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 5 if the number ends with 0 or 5.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 65 are 65, 130, 195, 260, etc.
- Integers: Integers are numbers that include all the whole numbers, negative numbers, and zero.
- Addition: Addition is a process of finding out the sum of two or more numbers.
- Absolute value: The absolute value of a number is its non-negative value, irrespective of its sign.
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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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