161 LearnersLast updated on May 26th, 2025
Divisibility Rule of 675
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 675.
What is the Divisibility Rule of 675?
The divisibility rule for 675 is a method by which we can find out if a number is divisible by 675 or not without using the division method.
Check whether 1350 is divisible by 675 with the divisibility rule.
Step 1: Verify if the number is divisible by 5. A number is divisible by 5 if its last digit is either 0 or 5. In 1350, the last digit is 0. Hence, it is divisible by 5.
Step 2: Verify if the number is divisible by 9. A number is divisible by 9 if the sum of its digits is divisible by 9. In 1350, the sum of the digits is 1 + 3 + 5 + 0 = 9, which is divisible by 9.
Step 3: Verify if the number is divisible by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 1350 is 9, which is divisible by 3.
Since 1350 is divisible by 5, 9, and 3, it is divisible by 675.
Tips and Tricks for Divisibility Rule of 675
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 675.
- Know the multiples of 675: Memorize the multiples of 675 (675, 1350, 2025, 2700, etc.) to quickly check divisibility. If the result from the checks is a multiple of 675, then the number is divisible by 675.
- 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 675
The divisibility rule of 675 helps us to quickly check if the given number is divisible by 675, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps by checking divisibility by 5, 9, and 3.
Divisibility Rule of 675 Examples
Problem 1
Is 6750 divisible by 675?
Yes, 6750 is divisible by 675.
Explanation
To determine if 6750 is divisible by 675, consider the fact that 675 = 5 × 5 × 3 × 3 × 3, and check if 6750 can be evenly divided by these factors.
1) Check divisibility by 25 (5 × 5): The last two digits of 6750 are 50, which is divisible by 25.
2) Check divisibility by 27 (3 × 3 × 3): Sum the digits of 6750 (6 + 7 + 5 + 0 = 18), and since 18 is divisible by 9, 6750 is divisible by 27.
3) Therefore, 6750 is divisible by 675.
Problem 2
Can 13500 be divided by 675 without leaving a remainder?
Yes, 13500 can be divided by 675 without a remainder.
Explanation
To verify, we need to ensure that 13500 passes the divisibility checks for 25 and 27, as explained above.
1) Divisibility by 25: The last two digits, 00, are divisible by 25.
2) Divisibility by 27: Sum the digits (1 + 3 + 5 + 0 + 0 = 9), and 9 is divisible by 9, confirming divisibility by 27.
3) Therefore, 13500 is divisible by 675.
Problem 3
Is 4725 divisible by 675?
No, 4725 is not divisible by 675.
Explanation
Check divisibility by 25 and 27.
1) Divisibility by 25: The last two digits, 25, are divisible by 25.
2) Divisibility by 27: Sum the digits (4 + 7 + 2 + 5 = 18), which is divisible by 9, but check 4725 ÷ 27 = 175, which is not an integer.
3) Since 4725 is not divisible by 27, it is not divisible by 675.
Problem 4
Is -5400 divisible by 675?
Yes, -5400 is divisible by 675.
Explanation
Ignore the negative sign and check the divisibility of 5400.
1) Divisibility by 25: The last two digits, 00, are divisible by 25.
2) Divisibility by 27: Sum the digits (5 + 4 + 0 + 0 = 9), and 9 is divisible by 9, confirming divisibility by 27.
3) Therefore, 5400, and hence -5400, is divisible by 675.
Problem 5
Can 8100 pass the divisibility rule of 675?
Yes, 8100 can pass the divisibility rule of 675.
Explanation
Check for divisibility by 25 and 27.
1) Divisibility by 25: The last two digits, 00, are divisible by 25.
2) Divisibility by 27: Sum the digits (8 + 1 + 0 + 0 = 9), and 9 is divisible by 9, confirming divisibility by 27.
3) Therefore, 8100 is divisible by 675.
FAQs on Divisibility Rule of 675
1.What is the divisibility rule for 675?
2.How many numbers are there between 1 and 10,000 that are divisible by 675?
3.Is 2025 divisible by 675?
4.What if I get 0 during the checks?
5.Does the divisibility rule of 675 apply to all integers?
6.How can children in Saudi Arabia use numbers in everyday life to understand Divisibility Rule of 675?
7.What are some fun ways kids in Saudi Arabia can practice Divisibility Rule of 675 with numbers?
8.What role do numbers and Divisibility Rule of 675 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Divisibility Rule of 675 skills?
Important Glossaries for Divisibility Rule of 675
- Divisibility rule: A set of rules used to find out whether a number is divisible by another number without performing division.
- Multiples: The results obtained after multiplying a number by an integer. For example, multiples of 675 are 675, 1350, 2025, etc.
- Integer: Numbers that include all whole numbers, negative numbers, and zero.
- Sum of digits: The total obtained by adding all the digits of a number.
- Verification: Checking the correctness of results by applying a known method, such as division, to confirm divisibility.
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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.
