235 LearnersLast updated on May 26th, 2025
Divisibility Rule of 525
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 525.
What is the Divisibility Rule of 525?
The divisibility rule for 525 is a method by which we can find out if a number is divisible by 525 or not without using the division method.
To check whether a number is divisible by 525, it must be divisible by 3, 5, and 7, since 525 = 3 × 5 × 7.
Example: Check whether 3675 is divisible by 525 with the divisibility rule.
1. Divisibility by 3: Add up the digits of the number. If the sum is divisible by 3, then the number is divisible by 3. For 3675, 3+6+7+5=21, and 21 is divisible by 3.
2. Divisibility by 5: Check if the last digit of the number is 0 or 5. For 3675, the last digit is 5, so it is divisible by 5.
3. Divisibility by 7: Multiply the last digit by 2 and subtract it from the rest of the number. Repeat if necessary. For 3675, multiply 5 by 2 to get 10, and subtract from 367 to get 357. Repeat the process: multiply 7 by 2 to get 14 and subtract from 35 to get 21. Since 21 is divisible by 7, 3675 is divisible by 7.
Since 3675 is divisible by 3, 5, and 7, it is divisible by 525.
Tips and Tricks for Divisibility Rule of 525
Knowing the individual rules for 3, 5, and 7 will help in mastering the divisibility rule for 525. Let's learn a few tips and tricks for this rule.
1. Know the multiples of 3, 5, and 7:
Memorizing these multiples will allow you to quickly verify divisibility.
2. Use the negative numbers:
If the result you get after using the divisibility rule for 7 is negative, ignore the symbol and consider it as positive for checking divisibility.
3. Repeat the process for large numbers:
For large numbers, you may need to repeat the divisibility check for 7 until you reach a smaller number.
4. Use the division method to verify:
You can use the division method to verify and cross-check your results.
Common Mistakes and How to Avoid Them in Divisibility Rule of 525
The divisibility rule of 525 helps us to quickly check if a given number is divisible by 525, but common mistakes like calculation errors can lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking divisibility by all three numbers (3, 5, and 7).
Ensure you check divisibility by 3, 5, and 7, as all conditions must be satisfied for divisibility by 525.
Mistake 2
Including the last digit in subtraction for the rule of 7.
Remember to exclude the last digit when subtracting after multiplying it by 2.
Mistake 3
Not repeating the process for divisibility by 7 when the result is large.
Repeat the process until a smaller, more manageable number is achieved.
Mistake 4
Not considering negative results for divisibility by 7.
Consider negative results as positive when checking for divisibility by 7.
Mistake 5
Confusing the steps for each divisibility rule.
Practice regularly to become familiar with the distinct steps for each rule.
Divisibility Rule of 525 Examples
Problem 1
Is 2100 divisible by 525?
Yes, 2100 is divisible by 525.
Explanation
To determine if 2100 is divisible by 525, we need to check divisibility by 5, 21, and 25, since 525 = 5 × 21 × 5.
Divisibility by 5: The number ends in 0, which means it is divisible by 5.
Divisibility by 21:
- Check divisibility by 3: Sum of digits = 2 + 1 + 0 + 0 = 3, which is divisible by 3.
- Check divisibility by 7: Double the last digit (0) and subtract from the remaining number (210), 21 - 0 = 21, which is divisible by 7.
Divisibility by 25: The last two digits are 00, which is divisible by 25.
Since 2100 is divisible by all these numbers, it is divisible by 525.
Problem 2
Check the divisibility rule of 525 for 5250.
Yes, 5250 is divisible by 525.
Explanation
To check divisibility by 525, verify divisibility by 5, 21, and 25.
Divisibility by 5: The number ends in 0, so it's divisible by 5.
Divisibility by 21:
- Check divisibility by 3: Sum of digits = 5 + 2 + 5 + 0 = 12, which is divisible by 3.
- Check divisibility by 7: Double the last digit (0) and subtract from the rest (525), 52 - 0 = 52, which is not divisible by 7, so double again, 10 - 4 = 6, not divisible. But 52 is divisible by 7.
Divisibility by 25: The last two digits are 50, which is divisible by 25.
Since all conditions are met, 5250 is divisible by 525.
Problem 3
Is 3675 divisible by 525?
No, 3675 is not divisible by 525.
Explanation
Check for divisibility by 5, 21, and 25.
1) Divisibility by 5: The number ends in 5, so it is divisible by 5.
2) Divisibility by 21:
- Check divisibility by 3: Sum of digits = 3 + 6 + 7 + 5 = 21, which is divisible by 3.
- Check divisibility by 7: Double the last digit (5) and subtract from the rest (367), 36 - 10 = 26, not divisible by 7.
3) Divisibility by 25: The last two digits are 75, which is not divisible by 25.
Since 3675 does not meet all conditions, it is not divisible by 525.
Problem 4
Can 10500 be divisible by 525 following the divisibility rule?
Yes, 10500 is divisible by 525.
Explanation
Verify divisibility by 5, 21, and 25.
1) Divisibility by 5: The number ends in 0, so it is divisible by 5.
2) Divisibility by 21:
- Check divisibility by 3: Sum of digits = 1 + 0 + 5 + 0 + 0 = 6, which is divisible by 3.
- Check divisibility by 7: Double the last digit (0) and subtract from the rest (1050), 105 - 0 = 105, which is divisible by 7.
3) Divisibility by 25: The last two digits are 00, which is divisible by 25.
All conditions are satisfied, so 10500 is divisible by 525.
Problem 5
Check the divisibility rule of 525 for 7875.
No, 7875 is not divisible by 525.
Explanation
Check for divisibility by 5, 21, and 25.
1) Divisibility by 5: The number ends in 5, so it is divisible by 5.
2) Divisibility by 21:
- Check divisibility by 3: Sum of digits = 7 + 8 + 7 + 5 = 27, which is divisible by 3.
- Check divisibility by 7: Double the last digit (5) and subtract from the rest (787), 78 - 10 = 68, which is not divisible by 7.
3) Divisibility by 25: The last two digits are 75, which is not divisible by 25.
Since 7875 does not meet all conditions, it is not divisible by 525.
FAQs on Divisibility Rule of 525
1.What is the divisibility rule for 525?
2. How many numbers between 1 and 1000 are divisible by 525?
3. Is 105 divisible by 525?
4. What if I get 0 after applying any divisibility rule?
5. Does the divisibility rule of 525 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 525?
7.What are some fun ways kids in United States can practice Divisibility Rule of 525 with numbers?
8.What role do numbers and Divisibility Rule of 525 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 525 skills?
Important Glossaries for Divisibility Rule of 525
- Divisibility rule: A set of rules used to determine if a number is divisible by another number without performing division.
- Multiples: Results obtained by multiplying a number by integers. For example, multiples of 5 are 5, 10, 15, etc.
- Integers: Whole numbers, including negative numbers, zero, and positive numbers.
- Subtraction: The process of finding the difference between two numbers by reducing one number from another.
- Verification: The process of confirming the correctness of a result, often using another method like division.
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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.
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