187 LearnersLast updated on May 26th, 2025
Divisibility Rule of 120
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 120.
What is the Divisibility Rule of 120?
The divisibility rule for 120 is a method by which we can find out if a number is divisible by 120 or not without using the division method. Check whether 2400 is divisible by 120 with the divisibility rule.
Step 1: Check if the number is divisible by 8. For 2400, check the last three digits, which are 400. Since 400 is divisible by 8 (400/8 = 50), proceed to the next step.
Step 2: Check if the number is divisible by 3. Sum the digits of 2400 (2 + 4 + 0 + 0 = 6). Since 6 is divisible by 3, proceed to the next step.
Step 3: Check if the number is divisible by 5. The last digit of 2400 is 0, which is divisible by 5.
Since 2400 satisfies all three conditions, it is divisible by 120.
Tips and Tricks for Divisibility Rule of 120
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 120.
- Know the prime factorization: Memorize that 120 = 2^3 × 3 × 5 to understand the divisibility requirements (by 8, 3, and 5).
- Use the divisibility of smaller numbers: Check divisibility by 8, 3, and 5 separately instead of 120 directly. This simplifies the process.
- Repeat the process for large numbers: Students should keep repeating the divisibility process for large numbers until they confirm divisibility by 8, 3, and 5.
- Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 120
The divisibility rule of 120 helps us quickly check if a given number is divisible by 120, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not checking all conditions.
Students should ensure they check divisibility by 8, 3, and 5.
Divisibility Rule of 120 Examples
Problem 1
A factory produces 240 widgets each day, and they are packed into boxes containing 120 widgets each. Does the production number allow for complete packing into boxes of 120 widgets?
Yes, 240 is divisible by 120.
Explanation
To check divisibility by 120, a number must be divisible by 3, 4, and 5.
1) For divisibility by 3, the sum of the digits of 240 is 2 + 4 + 0 = 6, which is divisible by 3.
2) For divisibility by 4, the last two digits are 40, and 40 is divisible by 4.
3) For divisibility by 5, the last digit is 0, which is divisible by 5.
As 240 meets all these conditions, it is divisible by 120.
Problem 2
A conference has 360 attendees, and each group discussion session can accommodate 120 participants. Is it possible to divide the attendees exactly into sessions with no one left out?
Yes, 360 is divisible by 120.
Explanation
To determine if 360 is divisible by 120, check divisibility by 3, 4, and 5:
1) The sum of the digits of 360 is 3 + 6 + 0 = 9, which is divisible by 3.
2) The last two digits are 60, and 60 is divisible by 4.
3) The last digit is 0, which is divisible by 5.
Since all conditions are satisfied, 360 is divisible by 120.
Problem 3
Suppose a library has 480 books to arrange on shelves, each capable of holding 120 books. Can the books be evenly distributed on the shelves?
Yes, 480 is divisible by 120.
Explanation
To check if 480 is divisible by 120, verify divisibility by 3, 4, and 5:
1) The sum of the digits of 480 is 4 + 8 + 0 = 12, which is divisible by 3.
2) The last two digits are 80, and 80 is divisible by 4.
3) The last digit is 0, which is divisible by 5.
Thus, 480 is divisible by 120.
Problem 4
A theater has 520 seats and plans to distribute tickets in groups of 120. Can the tickets be evenly distributed without any remaining?
No, 520 is not divisible by 120.
Explanation
To determine if 520 is divisible by 120, check divisibility by 3, 4, and 5:
1) The sum of the digits of 520 is 5 + 2 + 0 = 7, which is not divisible by 3.
2) The last two digits are 20, and 20 is divisible by 4.
3) The last digit is 0, which is divisible by 5.
Since 520 is not divisible by 3, it is not divisible by 120.
Problem 5
During a festival, 600 people are to be seated, with each tent accommodating 120 individuals. Can everyone be seated without any leftover spaces?
Yes, 600 is divisible by 120.
Explanation
To verify if 600 can be evenly divided by 120, check divisibility by 3, 4, and 5:
1) The sum of the digits of 600 is 6 + 0 + 0 = 6, which is divisible by 3.
2) The last two digits are 00, which is divisible by 4.
3) The last digit is 0, which is divisible by 5.
Since 600 satisfies all these conditions, it is divisible by 120.
FAQs on Divisibility Rule of 120
1.What is the divisibility rule for 120?
2.How many numbers are there between 1 and 1000 that are divisible by 120?
3.Is 360 divisible by 120?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 120 apply to all the integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 120?
7.What are some fun ways kids in United States can practice Divisibility Rule of 120 with numbers?
8.What role do numbers and Divisibility Rule of 120 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 120 skills?
Important Glossaries for Divisibility Rule of 120
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Prime factorization: Expressing a number as the product of its prime factors.
- Sum of digits: The sum of all individual digits in a number.
- Multiple: The result of multiplying a number by an integer.
- Integer: Numbers that include all whole numbers, negative numbers, and 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.
