196 LearnersLast updated on May 26th, 2025
Divisibility Rule of 945
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 945.
What is the Divisibility Rule of 945?
The divisibility rule for 945 is a method by which we can find out if a number is divisible by 945 or not without using the division method. To determine if a number is divisible by 945, it must be divisible by 3, 5, and 7, since 945 = 3 × 5 × 7 × 9. Check whether 2835 is divisible by 945 with the divisibility rule.
Step 1: Check divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. For 2835, 2 + 8 + 3 + 5 = 18, which is divisible by 3.
Step 2: Check divisibility by 5. A number is divisible by 5 if it ends in 0 or 5. Since 2835 ends in 5, it is divisible by 5.
Step 3: Check divisibility by 7. Use the divisibility rule of 7. Multiply the last digit by 2, and subtract it from the rest of the number. For 2835, 5 × 2 = 10, and 283 - 10 = 273. Repeat the process: 3 × 2 = 6, and 27 - 6 = 21. Since 21 is a multiple of 7, 2835 is divisible by 7.
Since 2835 is divisible by 3, 5, and 7, it is divisible by 945.
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Tips and Tricks for Divisibility Rule of 945
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 945.
Know the prime factors:
Memorize the prime factors of 945 (3, 5, 7) to quickly check divisibility.
Check each factor:
To determine divisibility by 945, a number must be divisible by each of its prime factors (3, 5, and 7).
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 verify their results and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 945
The divisibility rule of 945 helps us quickly check if a given number is divisible by 945, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you avoid them.
Mistake 1
Not checking all factors.
Ensure that the number is divisible by 3, 5, and 7, as all these factors are required.
Mistake 2
Confusing the steps.
Practice regularly to avoid confusion and remember the steps clearly.
Mistake 3
Not verifying with all factors.
Verify divisibility with all three factors to ensure accuracy.
Mistake 4
Not repeating the process when the result is large.
Students often stop the process after they have got a large result after addition. The process should be repeated until we get the smallest number that is divisible by 945.
Mistake 5
Incorrect multiplication of groups.
Ensure each group is multiplied by the correct integer, starting from 1 for the rightmost group.
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Divisibility Rule of 945 Examples
Problem 1
Can 4725 be divisible by 945?
Yes, 4725 is divisible by 945.
Explanation
To check if 4725 is divisible by 945, it must be divisible by 3, 5, and 7, since 945 = 3 × 5 × 7 × 9.
1) Divisibility by 3: Sum the digits: 4 + 7 + 2 + 5 = 18, and 18 is divisible by 3.
2) Divisibility by 5: The last digit is 5, which is a multiple of 5.
3) Divisibility by 7:
Double the last digit: 5 × 2 = 10.
Subtract from remaining: 472 - 10 = 462.
Repeat: 2 × 2 = 4, 46 - 4 = 42.
42 is a multiple of 7.
Since 4725 is divisible by 3, 5, and 7, it is divisible by 945.
Problem 2
Is 1890 divisible by 945?
No, 1890 is not divisible by 945.
Explanation
For 1890 to be divisible by 945, it must pass the tests for divisibility by 3, 5, and 7.
1) Divisibility by 3: Sum the digits: 1 + 8 + 9 + 0 = 18, and 18 is divisible by 3.
2) Divisibility by 5: The last digit is 0, which is a multiple of 5.
3) Divisibility by 7:
Double the last digit: 0 × 2 = 0.
Subtract from remaining: 189 - 0 = 189.
Double the last digit of 189: 9 × 2 = 18.
Subtract: 18 - 18 = 0.
0 is a multiple of 7.
Though 1890 is divisible by 3, 5, and 7, it must also be divisible by 9 (since 945 = 3^3 × 5 × 7), but 1 + 8 + 9 + 0 = 18, and 18 is not divisible by 9. Therefore, 1890 is not divisible by 945.
Problem 3
Check if -2835 is divisible by 945.
Yes, -2835 is divisible by 945.
Explanation
To determine if -2835 is divisible by 945, we check divisibility by 3, 5, and 7.
1) Divisibility by 3: Sum the digits: 2 + 8 + 3 + 5 = 18, and 18 is divisible by 3.
2) Divisibility by 5: The last digit is 5, which is a multiple of 5.
3) Divisibility by 7:
Double the last digit: 5 × 2 = 10.
Subtract from remaining: 283 - 10 = 273.
Double last digit of 273: 3 × 2 = 6.
Subtract: 27 - 6 = 21.
21 is a multiple of 7.
Since -2835 is divisible by 3, 5, and 7, it is divisible by 945.
Problem 4
Determine if 1134 is divisible by 945.
No, 1134 is not divisible by 945.
Explanation
To check if 1134 is divisible by 945, it must be divisible by 3, 5, and 7.
1) Divisibility by 3: Sum the digits: 1 + 1 + 3 + 4 = 9, and 9 is divisible by 3.
2) Divisibility by 5: The last digit is 4, which is not a multiple of 5.
Since 1134 fails the divisibility test for 5, it cannot be divisible by 945.
Problem 5
Verify the divisibility of 2835 by 945.
Yes, 2835 is divisible by 945.
Explanation
To verify divisibility by 945, check divisibility by 3, 5, and 7.
1) Divisibility by 3: Sum the digits: 2 + 8 + 3 + 5 = 18, and 18 is divisible by 3.
2) Divisibility by 5: The last digit is 5, which is a multiple of 5.
3) Divisibility by 7:
Double the last digit: 5 × 2 = 10.
Subtract from remaining: 283 - 10 = 273.
Double last digit of 273: 3 × 2 = 6.
Subtract: 27 - 6 = 21.
21 is a multiple of 7.
Since 2835 is divisible by 3, 5, and 7, it is divisible by 945.
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FAQs on Divisibility Rule of 945
1.What is the divisibility rule for 945?
2.How many numbers are there between 1 and 1000 that are divisible by 945?
3.Is 2835 divisible by 945?
4.What if I get 0 during any divisibility check?
5.Does the divisibility rule of 945 apply to all integers?
6.How can children in Canada use numbers in everyday life to understand Divisibility Rule of 945?
7.What are some fun ways kids in Canada can practice Divisibility Rule of 945 with numbers?
8.What role do numbers and Divisibility Rule of 945 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Divisibility Rule of 945 skills?
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Important Glossaries for Divisibility Rule of 945
- Divisibility rule: A set of guidelines used to determine if a number is divisible by another number without performing division.
- Prime factors: The smallest primes that multiply together to make a given number. For 945, these are 3, 5, and 7.
- Multiples: The results obtained by multiplying a number by integers. For example, multiples of 945 include 945, 1890, etc.
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: The process of finding the difference between two numbers by reducing one from the other.
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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.
