183 LearnersLast updated on May 26th, 2025
Divisibility Rule of 480
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 480.
What is the Divisibility Rule of 480?
The divisibility rule for 480 is a method by which we can find out if a number is divisible by 480 or not without using the division method. To determine if a number is divisible by 480, it must be divisible by all the prime factors of 480. The prime factorization of 480 is 2^5 × 3 × 5.
1. Divisibility by 16 (2^4): The last four digits of the number must be divisible by 16.
2. Divisibility by 3: The sum of the digits of the number must be divisible by 3.
3. Divisibility by 5: The number must end in 0.
Let's check whether 3840 is divisible by 480 with the divisibility rule.
Step 1: Check divisibility by 16. The last four digits are 3840. Check if 3840 is divisible by 16. 3840 ÷ 16 = 240, which is an integer, so 3840 is divisible by 16.
Step 2: Check divisibility by 3. Add the digits: 3 + 8 + 4 + 0 = 15. Since 15 is divisible by 3, 3840 is divisible by 3.
Step 3: Check divisibility by 5. The number ends in 0, so it is divisible by 5.
Since 3840 passes all these tests, it is divisible by 480.
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Tips and Tricks for Divisibility Rule of 480
Learn divisibility rules to help master division. Let’s learn a few tips and tricks for the divisibility rule of 480.
- Know the multiples of prime factors: Memorize the multiples of 16, 3, and 5 to quickly check divisibility.
- Use smaller numbers: Break down large numbers into smaller parts to test each divisibility rule.
- Repeat the process for large numbers: For very large numbers, break them down and check the rules for smaller sections.
- Use the division method to verify: Always use the division method to verify and cross-check results, which will help to confirm calculations.
Common Mistakes and How to Avoid Them in Divisibility Rule of 480
The divisibility rule of 480 helps us to quickly check if a given number is divisible by 480, but common mistakes can lead to incorrect calculations. Here are some common mistakes and how to avoid them.
Mistake 1
Not checking all prime factors.
Ensure each divisibility rule (16, 3, and 5) is checked for comprehensive testing.
Mistake 2
Incorrectly applying divisibility rules.
Follow each step separately and carefully to ensure correct application for each prime factor.
Mistake 3
Forgetting to check divisibility by 16.
Remember to always check the last four digits for divisibility by 16.
Mistake 4
Ignoring the ending digit for divisibility by 5.
Always check if the number ends in 0 for divisibility by 5.
Mistake 5
Confusing the steps.
Practice regularly to memorize the correct sequence of steps.
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Divisibility Rule of 480 Examples
Problem 1
Is the number of pages in a book, 960, divisible by 480?
Yes, 960 is divisible by 480.
Explanation
To verify, we divide 960 by 480. The result is 2, a whole number, indicating that 960 is divisible by 480.
Problem 2
A shipment contains 1440 items. Can they be equally distributed among 480 boxes?
Yes, 1440 items can be equally distributed among 480 boxes.
Explanation
When you divide 1440 by 480, the quotient is 3, which is a whole number, demonstrating that 1440 is divisible by 480.
Problem 3
A concert venue has a seating capacity of 720. Is this number divisible by 480?
No, 720 is not divisible by 480.
Explanation
Dividing 720 by 480 gives a quotient of 1.5, which is not a whole number, indicating that 720 is not divisible by 480.
Problem 4
A company has a total of 1920 employees. If they want to form teams of 480, will each team have an equal number of employees?
Yes, 1920 employees can be divided into teams of 480 equally.
Explanation
Dividing 1920 by 480 results in a quotient of 4, which is a whole number, showing that 1920 is divisible by 480.
Problem 5
Is the total distance of 2400 miles divisible by 480 miles per day for a road trip?
Yes, 2400 miles is divisible by 480.
Explanation
When you divide 2400 by 480, the quotient is 5, a whole number, which means 2400 miles is divisible by 480 miles per day.
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FAQs on Divisibility Rule of 480
1.What is the divisibility rule for 480?
2.How many numbers are there between 1 and 1000 that are divisible by 480?
3.Is 1440 divisible by 480?
4.What if I get 0 when checking divisibility by 3?
5.Does the divisibility rule of 480 apply to all integers?
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Important Glossaries for Divisibility Rule of 480:
- Divisibility rule: A set of rules used to determine if a number is divisible by another number without performing division.
- Prime factors: The prime numbers that multiply together to give a number. For 480, these are 2, 3, and 5.
- Multiples: The results obtained by multiplying a number by integers. For example, multiples of 16 include 16, 32, 48, etc.
- Integer: A whole number that can be positive, negative, or zero.
- Factorization: The process of breaking down a number into its prime factors.
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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.
