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112 LearnersLast updated on February 16th, 2025
Divisibility Rule of 645
The divisibility rule is a way to determine whether a number is divisible by another number without performing the division operation. In real life, we can use divisibility rules for quick calculations, dividing things evenly, and organizing items. In this topic, we will learn about the divisibility rule of 645.
What is the Divisibility Rule of 645?
The divisibility rule for 645 is a method by which we can determine if a number is divisible by 645 without performing the division operation. Check whether 1290 is divisible by 645 with the divisibility rule.
Step 1: Check divisibility by 5. A number is divisible by 5 if it ends in 0 or 5. Here, 1290 ends with 0, so it is divisible by 5.
Step 2: Check divisibility by 129, as 645 = 5 × 129. Divide the number obtained by removing the last digit by 2 (since 129 is divisible by 3 after checking its sum of digits, 1 + 2 + 9 = 12, which is divisible by 3). So, 129 → 12. Remove the last digit of 1290 to get 129, and divide by 2 → 12 / 2 = 6. Check if the result, 6, is a multiple of 129.
Step 3: As 6 is not divisible by 129, 1290 is not divisible by 645.
Tips and Tricks for Divisibility Rule of 645
Learning divisibility rules will help students master division. Let’s learn a few tips and tricks for the divisibility rule of 645.
- Know the multiples of 645: Memorize the multiples of 645 (645, 1290, 1935, ...etc.) to quickly check divisibility. If the result from subtraction or division is a multiple of 645, then the number is divisible by 645.
- Use negative numbers wisely: If the result obtained after subtraction is negative, consider it as positive for checking divisibility.
- Repeat the process for large numbers: Continue the divisibility process until you reach a small number that is divisible by 645.
For example: Check if 7745 is divisible by 645 using the divisibility test.
Check divisibility by 5; since 7745 ends with 5, it is divisible by 5.
Remove the last digit to get 774, and check divisibility by 129 using the same steps as above.
Since 774 is not divisible by 129, 7745 is not divisible by 645.
- Use the division method to verify: Use the division method as a way to verify and crosscheck results. This helps in verification and learning.
Common Mistakes and How to Avoid Them in Divisibility Rule of 645
The divisibility rule of 645 helps us quickly check if a given number is divisible by 645, but common mistakes, such as calculation errors, can lead to incorrect conclusions. Here, we will understand some common mistakes and how to avoid them.
Mistake 1
Follow the correct steps: check divisibility by 5, then remove the last digit and divide by 2, and check if the result is a multiple of 129.
Divisibility Rule of 645 Examples
Problem 1
Is 1935 divisible by 645?
No, 1935 is not divisible by 645.
Explanation
To check if 1935 is divisible by 645, we can use the divisibility rule for 645, which is a combination of the rules for 5, 3, and 43.
1) Check divisibility by 5: The number ends in 5, so it is divisible by 5.
2) Check divisibility by 3: The sum of the digits is 18 (1 + 9 + 3 + 5), which is divisible by 3.
3) Check divisibility by 43: Divide 1935 by 43. The result is not an integer.
Therefore, 1935 is not divisible by 645.
Problem 2
Check the divisibility rule of 645 for 3225.
Yes, 3225 is divisible by 645.
Explanation
To check if 3225 is divisible by 645, we apply the rules for 5, 3, and 43.
1) Check divisibility by 5: The number ends in 5, so it is divisible by 5.
2) Check divisibility by 3: The sum of the digits is 12 (3 + 2 + 2 + 5), which is divisible by 3.
3) Check divisibility by 43: Divide 3225 by 43. The result is an integer.
Therefore, 3225 is divisible by 645.
Problem 3
Is -6450 divisible by 645?
Yes, -6450 is divisible by 645.
Explanation
To determine if -6450 is divisible by 645, remove the negative sign and check the number.
1) Check divisibility by 5: The number ends in 0, so it is divisible by 5.
2) Check divisibility by 3: The sum of the digits is 15 (6 + 4 + 5 + 0), which is divisible by 3.
3) Check divisibility by 43: Divide 6450 by 43. The result is an integer.
Thus, -6450 is divisible by 645.
Problem 4
Can 2580 be divisible by 645 following the divisibility rule?
No, 2580 is not divisible by 645.v
Explanation
To check if 2580 is divisible by 645, we follow the divisibility rules for 5, 3, and 43.
1) Check divisibility by 5: The number ends in 0, so it is divisible by 5.
2) Check divisibility by 3: The sum of the digits is 15 (2 + 5 + 8 + 0), which is divisible by 3.
3) Check divisibility by 43: Divide 2580 by 43. The result is not an integer.
Therefore, 2580 is not divisible by 645.
Problem 5
Check the divisibility rule of 645 for 1290
No, 1290 is not divisible by 645.
Explanation
To verify if 1290 is divisible by 645, we check the divisibility by 5, 3, and 43.
1) Check divisibility by 5: The number ends in 0, so it is divisible by 5.
2) Check divisibility by 3: The sum of the digits is 12 (1 + 2 + 9 + 0), which is divisible by 3.
3) Check divisibility by 43: Divide 1290 by 43. The result is not an integer.
Thus, 1290 is not divisible by 645.
What is the divisibility rule for 645?
1.What is the divisibility rule for 645?
2.How many numbers are there between 1 and 10000 that are divisible by 645?
3.Is 3225 divisible by 645?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 645 apply to all integers?
Important Glossaries for Divisibility Rule of 645
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number without directly dividing.
- Multiples: Results obtained from multiplying a number by an integer. For example, multiples of 645 are 645, 1290, 1935, ...
- Integers: Numbers that include whole numbers, negative numbers, and zero.
- Subtraction: The process of finding the difference between two numbers by reducing one number from another.
- Division: A mathematical operation where a number is evenly distributed into equal parts.
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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.
