188 LearnersLast updated on May 26th, 2025
Divisibility Rule of 315
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 315.
What is the Divisibility Rule of 315?
The divisibility rule for 315 is a method by which we can find out if a number is divisible by 315 or not without using the division method. Check whether 630 is divisible by 315 with the divisibility rule.
Step 1: Check if the number is divisible by 5. Since 630 ends in 0, it is divisible by 5.
Step 2: Check if the number is divisible by 9. Add the digits of 630 (6 + 3 + 0 = 9). Since 9 is divisible by 9, 630 is divisible by 9.
Step 3: Check if the number is divisible by 7. Multiply the last digit by 2 (0 × 2 = 0) and subtract it from the rest of the number (63 - 0 = 63). Since 63 is divisible by 7, 630 is divisible by 7.
Since 630 is divisible by 5, 9, and 7, it is divisible by 315.
Tips and Tricks for Divisibility Rule of 315
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 315.
Know the multiples of 315:
Memorize the multiples of 315 (315, 630, 945, 1260, etc.) to quickly check divisibility.
Use the divisibility rules of 5, 9, and 7:
Ensure a number is divisible by each of these to confirm divisibility by 315.
Repeat the process for large numbers:
Students should keep repeating the divisibility process for each factor until they reach a small number that is divisible by all. For example, check if 1575 is divisible by 315. It ends in 5, so it's divisible by 5. The sum of its digits is 18, which is divisible by 9. Finally, using the rule for 7, 157 - (5 × 2) = 147, which is divisible by 7. So, 1575 is divisible by 315.
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 315
The divisibility rule of 315 helps us to quickly check if the given number is divisible by 315, 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 for each factor. S
Students should ensure they apply the correct divisibility rules for 5, 9, and 7
Divisibility Rule of 315 Examples
Problem 1
Is 945 divisible by 315?
Yes, 945 is divisible by 315.
Explanation
To check divisibility by 315, a number must be divisible by 5, 9, and 7.
1) Divisibility by 5: The last digit of 945 is 5, which is divisible by 5.
2) Divisibility by 9: Sum the digits, 9 + 4 + 5 = 18. Since 18 is divisible by 9, 945 is divisible by 9.
3) Divisibility by 7: Using the rule for 7:
Multiply the last digit by 2: 5 × 2 = 10.
Subtract from the rest of the number: 94 - 10 = 84.
84 is divisible by 7 (7 × 12 = 84).
All conditions are met, so 945 is divisible by 315.
Problem 2
Check if 2205 is divisible by 315.
Yes, 2205 is divisible by 315.
Explanation
To verify, check divisibility by 5, 9, and 7.
1) Divisibility by 5: The last digit is 5, thus divisible by 5.
2) Divisibility by 9: Sum of digits is 2 + 2 + 0 + 5 = 9, which is divisible by 9.
3) Divisibility by 7: Apply the rule:
Multiply the last digit by 2: 5 × 2 = 10.
Subtract from the rest: 220 - 10 = 210.
210 is divisible by 7 (7 × 30 = 210).
All criteria are satisfied, so 2205 is divisible by 315.
Problem 3
Is 1575 divisible by 315?
Yes, 1575 is divisible by 315.
Explanation
Check divisibility by 5, 9, and 7.
1) Divisibility by 5: The last digit is 5, hence divisible by 5.
2) Divisibility by 9: Sum of digits is 1 + 5 + 7 + 5 = 18, which is divisible by 9.
3) Divisibility by 7: Using the rule:
Multiply the last digit by 2: 5 × 2 = 10.
Subtract from the rest: 157 - 10 = 147.
147 is divisible by 7 (7 × 21 = 147).
All conditions are met, so 1575 is divisible by 315.
Problem 4
Can 1230 be divisible by 315?
No, 1230 is not divisible by 315.
Explanation
Check divisibility by 5, 9, and 7.
1) Divisibility by 5: The last digit is 0, so divisible by 5.
2) Divisibility by 9: Sum of digits is 1 + 2 + 3 + 0 = 6, which is not divisible by 9.
Since the number is not divisible by 9, it cannot be divisible by 315.
Problem 5
Check if 2835 is divisible by 315.
Yes, 2835 is divisible by 315.
Explanation
Verify divisibility by 5, 9, and 7.
1) Divisibility by 5: The last digit is 5, hence divisible by 5.
2) Divisibility by 9: Sum of digits is 2 + 8 + 3 + 5 = 18, which is divisible by 9.
3) Divisibility by 7: Applying the rule:
Multiply the last digit by 2: 5 × 2 = 10.
Subtract from the rest: 283 - 10 = 273.
273 divided by 7 gives an integer (7 × 39 = 273).
All conditions are satisfied, so 2835 is divisible by 315.
FAQs on Divisibility Rule of 315
1.What is the divisibility rule for 315?
2.How many numbers are there between 1 and 1000 that are divisible by 315?
3.Is 945 divisible by 315?
4. What if I get 0 after applying the divisibility rules?
5.Does the divisibility rule of 315 apply to all the integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 315?
7.What are some fun ways kids in United States can practice Divisibility Rule of 315 with numbers?
8.What role do numbers and Divisibility Rule of 315 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 315 skills?
Important Glossaries for Divisibility Rule of 315
- 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 it ends in 0 or 5.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example: multiples of 315 are 315, 630, 945, etc.
- Factors: Factors are numbers we multiply together to get another number. For example, 5, 9, and 7 are factors of 315.
- Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from 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.
