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116 LearnersLast updated on April 1st, 2025
Divisibility Rule of 60
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 items. In this topic, we will learn about the divisibility rule of 60.
What is the Divisibility Rule of 60?
The divisibility rule for 60 is a method by which we can determine if a number is divisible by 60 without using the division method. A number is divisible by 60 if it is divisible by its prime factors: 2, 3, and 5. Check whether 240 is divisible by 60 with the divisibility rule.
Step 1: Check if the number is divisible by 2. A number is divisible by 2 if its last digit is even. In 240, the last digit is 0, which is even.
Step 2: Check if the number is divisible by 3. Add all the digits of the number, and if the sum is divisible by 3, then the number is divisible by 3. For 240, 2 + 4 + 0 = 6, which is divisible by 3.
Step 3: Check if the number is divisible by 5. A number is divisible by 5 if its last digit is 0 or 5. In 240, the last digit is 0.
Since 240 is divisible by 2, 3, and 5, it is divisible by 60.
Tips and Tricks for Divisibility Rule of 60
Learning the divisibility rule will help kids master division. Let’s explore a few tips and tricks for the divisibility rule of 60.
Know the divisibility rules of 2, 3, and 5:
Memorize these rules, as a number must be divisible by all three to be divisible by 60.
Use the prime factorization:
60 = 2 × 2 × 3 × 5. Ensure the number is divisible by each of these factors.
Combine smaller rules:
Check divisibility by 6 (2 and 3) and then by 5. If both are satisfied, the number is divisible by 60.
Use the division method to verify:
Students can use the division method to verify and crosscheck their results. This will help them to confirm their findings and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 60
The divisibility rule of 60 helps us quickly check if a given number is divisible by 60, but common mistakes like calculation errors can lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking all the rules.
Ensure you check divisibility by 2, 3, and 5, as all are required for divisibility by 60.
Divisibility Rule of 60 Examples
Problem 1
Is the number of pages in a book, 180, divisible by 60?
Yes, 180 is divisible by 60.
Explanation
To check if 180 is divisible by 60, the number must be divisible by both 5 and 12 (since 60 = 5 × 12).
1) Check divisibility by 5: The last digit of 180 is 0, which is divisible by 5.
2) Check divisibility by 12: A number is divisible by 12 if it is divisible by both 3 and 4.
To check divisibility by 3, sum the digits: 1 + 8 + 0 = 9. Since 9 is divisible by 3, 180 is divisible by 3.
To check divisibility by 4, look at the last two digits: 80. Since 80 is divisible by 4, 180 is divisible by 4.
Since 180 is divisible by both 5 and 12, it is divisible by 60.
Problem 2
A factory produces 240 widgets per batch. Is 240 divisible by 60?
Yes, 240 is divisible by 60
Explanation
To determine if 240 is divisible by 60, check for divisibility by 5 and 12.
1) Divisibility by 5: The last digit is 0, which means it is divisible by 5.
2) Divisibility by 12: Check divisibility by 3 and 4.
Sum of digits: 2 + 4 + 0 = 6, which is divisible by 3.
Last two digits: 40, which is divisible by 4.
Since 240 meets both criteria, it is divisible by 60.
Problem 3
A conference has 360 attendees. Can they be evenly divided into groups of 60?
Yes, 360 is divisible by 60.
Explanation
To verify, check divisibility by 5 and 12.
1) Divisibility by 5: The last digit is 0, so it is divisible by 5.
2) Divisibility by 12: Check divisibility by 3 and 4.
Sum of digits: 3 + 6 + 0 = 9, which is divisible by 3.
Last two digits: 60, which is divisible by 4.
Since 360 is divisible by both 5 and 12, it is divisible by 60.
Problem 4
Is the length of a ribbon, 250 centimeters, divisible by 60?
No, 250 is not divisible by 60.
Explanation
To check, evaluate divisibility by 5 and 12.4
1) Divisibility by 5: The last digit is 0, so it is divisible by 5.
2) Divisibility by 12: Check divisibility by 3 and 4.
Sum of digits: 2 + 5 + 0 = 7, which is not divisible by 3.
Since 250 is not divisible by 3, it cannot be divisible by 12, and thus not by 60.
Problem 5
A shipment contains 480 items. Are these items divisible into crates of 60?
Yes, 480 is divisible by 60.
Explanation
Check divisibility by 5 and 12.
1) Divisibility by 5: The last digit is 0, so it is divisible by 5.
2) Divisibility by 12: Check divisibility by 3 and 4.
Sum of digits: 4 + 8 + 0 = 12, which is divisible by 3.
Last two digits: 80, which is divisible by 4.
Since 480 is divisible by both 5 and 12, it is divisible by 60.
FAQs on Divisibility Rule of 60
1.What is the divisibility rule for 60?
2.How many numbers are there between 1 and 100 that are divisible by 60?
3.Is 300 divisible by 60?
4.What if I find the number divisible by 2 and 3 but not by 5?
5.Does the divisibility rule of 60 apply to all integers?
Important Glossaries for Divisibility Rule of 60
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Prime factors: The prime numbers that multiply together to give the original number. For example, the prime factors of 60 are 2, 3, and 5.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 60 are 60, 120, 180, etc.
- Sum of digits: The total obtained by adding all the digits of a number.
- Even numbers: Numbers that are divisible by 2. For example, 2, 4, 6, 8, etc.
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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.
