188 LearnersLast updated on May 26th, 2025
Divisibility Rule of 180
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 180.
What is the Divisibility Rule of 180?
The divisibility rule for 180 is a method to determine if a number is divisible by 180 without using the division method.
Step 1: Check if the number is divisible by 2. This means the number should be even (its last digit should be 0, 2, 4, 6, or 8).
Step 2: Check if the number is divisible by 3. This means that the sum of its digits should be divisible by 3.
Step 3: Check if the number is divisible by 5. This means the last digit of the number should be 0 or 5.
Step 4: If the number passes all these checks (divisible by 2, 3, and 5), then it is divisible by 180.
Example: Check whether 540 is divisible by 180 using the divisibility rule.
For divisibility by 2: 540 ends in 0, which is even.
For divisibility by 3: The sum of the digits is 5 + 4 + 0 = 9, and 9 is divisible by 3.
For divisibility by 5: 540 ends in 0, which is divisible by 5.
Since 540 satisfies all the above conditions, it is divisible by 180.
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Tips and Tricks for Divisibility Rule of 180
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 180.
- Know the combinations: Memorize the conditions for divisibility by 2, 3, and 5 to quickly check divisibility by 180.
- Repeat the process for large numbers: For large numbers, ensure each condition is checked, and if a number fails any one of the conditions, it is not divisible by 180.
- 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 180
The divisibility rule of 180 helps us quickly check if a given number is divisible by 180, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking all conditions.
Ensure the number is divisible by 2, 3, and 5 before concluding it is divisible by 180.
Mistake 2
Forgetting the divisibility by 3 check.
Always remember to check if the sum of the digits is divisible by 3.
Mistake 3
Confusing divisibility checks.
Practice regularly to avoid confusing the steps or forgetting to check a condition.
Mistake 4
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Mistake 5
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Divisibility Rule of 180 Examples
Problem 1
Can 720 be divided by 180 without a remainder?
Yes, 720 is divisible by 180.
Explanation
To check if 720 is divisible by 180, we need to confirm it meets the divisibility rules for 2, 3, and 5 (since 180 = 2 × 3 × 3 × 5).
1) Check for divisibility by 2: 720 ends in 0, which is even.
2) Check for divisibility by 3: Sum of digits 7 + 2 + 0 = 9, which is divisible by 3.
3) Check for divisibility by 5: 720 ends in 0.
All conditions are satisfied, so 720 is divisible by 180.
Problem 2
Is 4500 divisible by 180?
Yes, 4500 is divisible by 180.
Explanation
To determine if 4500 is divisible by 180, ensure it follows the divisibility rules for 2, 3, and 5.
1) Check for divisibility by 2: 4500 ends in 0, which is even.
2) Check for divisibility by 3: Sum of digits 4 + 5 + 0 + 0 = 9, which is divisible by 3.
3) Check for divisibility by 5: 4500 ends in 0.
All conditions are met, so 4500 is divisible by 180.
Problem 3
Verify if 1260 can be divided by 180 without leaving a remainder.
Yes, 1260 is divisible by 180.
Explanation
To check divisibility by 180, confirm divisibility by 2, 3, and 5.
1) Check for divisibility by 2: 1260 ends in 0, which is even.
2) Check for divisibility by 3: Sum of digits 1 + 2 + 6 + 0 = 9, which is divisible by 3.
3) Check for divisibility by 5: 1260 ends in 0.
Since all conditions are satisfied, 1260 is divisible by 180.
Problem 4
Is 1340 divisible by 180?
No, 1340 is not divisible by 180.
Explanation
To determine divisibility by 180, check for divisibility by 2, 3, and 5.
1) Check for divisibility by 2: 1340 ends in 0, which is even.
2) Check for divisibility by 3: Sum of digits 1 + 3 + 4 + 0 = 8, which is not divisible by 3.
3) Check for divisibility by 5: 1340 ends in 0.
The number fails the divisibility test for 3, so 1340 is not divisible by 180.
Problem 5
Determine if 1620 is divisible by 180.
Yes, 1620 is divisible by 180.
Explanation
For divisibility by 180, verify the divisibility rules for 2, 3, and 5.
1) Check for divisibility by 2: 1620 ends in 0, which is even.
2) Check for divisibility by 3: Sum of digits 1 + 6 + 2 + 0 = 9, which is divisible by 3.
3) Check for divisibility by 5: 1620 ends in 0.
All conditions are met, so 1620 is divisible by 180.
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FAQs on Divisibility Rule of 180
1.What is the divisibility rule for 180?
2.How many numbers between 1 and 1000 are divisible by 180?
3.Is 360 divisible by 180?
4.What if I miss one condition?
5. Does the divisibility rule of 180 apply to all integers?
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Important Glossaries for Divisibility Rule of 180
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number without performing division.
- Even number: A number that is divisible by 2.
- Multiple: The result of multiplying a number by an integer.
- Sum of digits: The sum obtained by adding all the digits in a number.
- Integer: A whole number; it can be positive, negative, or zero.
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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.
