Last updated on May 26th, 2025
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.
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.
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.
Memorizing these multiples will allow you to quickly verify divisibility.
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.
For large numbers, you may need to repeat the divisibility check for 7 until you reach a smaller number.
You can use the division method to verify and cross-check your results.
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.
Is 2100 divisible by 525?
Yes, 2100 is divisible by 525.
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.
Check the divisibility rule of 525 for 5250.
Yes, 5250 is divisible by 525.
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.
Is 3675 divisible by 525?
No, 3675 is not divisible by 525.
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.
Can 10500 be divisible by 525 following the divisibility rule?
Yes, 10500 is divisible by 525.
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.
Check the divisibility rule of 525 for 7875.
No, 7875 is not divisible by 525.
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.
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.
: She loves to read number jokes and games.