174 LearnersLast updated on May 26th, 2025
Divisibility Rule of 15
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 15.
What is the Divisibility Rule of 15?
The divisibility rule for 15 is a method by which we can find out if a number is divisible by 15 or not without using the division method. Check whether 345 is divisible by 15 with the divisibility rule.
Step 1: Check if the number is divisible by 3. Add the digits of the number, 3+4+5=12. Since 12 is divisible by 3, the number passes this part of the test.
Step 2: Check if the number is divisible by 5. Since 345 ends in 5, it is divisible by 5.
Step 3: As the number passes both tests (divisible by both 3 and 5), 345 is divisible by 15.
Tips and Tricks for Divisibility Rule of 15
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 15.
- Know the multiples of 15: Memorize the multiples of 15 (15, 30, 45, 60, 75, etc.) to quickly check the divisibility. If a number matches one of these multiples, it is divisible by 15.
- Break the rule into parts: Since 15 is the product of 3 and 5, check divisibility by both numbers separately to determine divisibility by 15.
- 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 verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 15
The divisibility rule of 15 helps us quickly check if a given number is divisible by 15, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking both divisibility rules (3 and 5).
Ensure to check both parts of the rule. A number must be divisible by both 3 and 5 to be divisible by 15.
Divisibility Rule of 15 Examples
Problem 1
A farmer has 360 apples and wants to pack them into boxes such that each box has an equal number of apples and there are exactly 15 boxes. Is it possible to do so?
Yes, 360 is divisible by 15.
Explanation
To check if 360 is divisible by 15, we use the rule that a number must be divisible by both 3 and 5.
1. Divisibility by 3: Sum the digits of 360: 3 + 6 + 0 = 9. Since 9 is divisible by 3, 360 is divisible by 3.
2. Divisibility by 5: The last digit of 360 is 0, which is divisible by 5.
Since 360 meets the criteria for divisibility by both 3 and 5, it is divisible by 15.
Problem 2
A baker is preparing 225 cupcakes and needs to package them into boxes such that each box contains 15 cupcakes. Can this be done without any cupcakes left over?
Yes, 225 is divisible by 15.
Explanation
To check if 225 is divisible by 15, it must be divisible by both 3 and 5.
1. Divisibility by 3: Sum the digits of 225: 2 + 2 + 5 = 9. Since 9 is divisible by 3, 225 is divisible by 3.
2. Divisibility by 5: The last digit of 225 is 5, which is divisible by 5.
Since 225 is divisible by both 3 and 5, it is also divisible by 15.
Problem 3
A librarian has 420 books to arrange on shelves where each shelf must have exactly 15 books. Can this be arranged perfectly?
Yes, 420 is divisible by 15.
Explanation
To determine if 420 is divisible by 15, it must be divisible by both 3 and 5.
1. Divisibility by 3: Sum the digits of 420: 4 + 2 + 0 = 6. Since 6 is divisible by 3, 420 is divisible by 3.
2. Divisibility by 5: The last digit of 420 is 0, which is divisible by 5.
Since 420 satisfies both conditions, it is divisible by 15.
Problem 4
An event planner has 310 chairs to arrange in rows with each row containing exactly 15 chairs. Is it possible to arrange them without any chairs left over?
No, 310 is not divisible by 15.
Explanation
To check if 310 is divisible by 15, it must be divisible by both 3 and 5.
1. Divisibility by 3: Sum the digits of 310: 3 + 1 + 0 = 4. Since 4 is not divisible by 3, 310 is not divisible by 3.
2. Divisibility by 5: The last digit of 310 is 0, which is divisible by 5.
Since 310 is not divisible by 3, it is not divisible by 15.
Problem 5
A school has 150 students to organize into teams where each team has exactly 15 students. Can the students be divided evenly?
Yes, 150 is divisible by 15.
Explanation
To verify if 150 is divisible by 15, check divisibility by both 3 and 5.
1. Divisibility by 3: Sum the digits of 150: 1 + 5 + 0 = 6. Since 6 is divisible by 3, 150 is divisible by 3.
2. Divisibility by 5: The last digit of 150 is 0, which is divisible by 5.
Since 150 is divisible by both 3 and 5, it is divisible by 15.
FAQs on Divisibility Rule of 15
1.What is the divisibility rule for 15?
2.How many numbers are there between 1 and 100 that are divisible by 15?
3.Is 45 divisible by 15?
4.What if a number is divisible by only one of 3 or 5?
5.Does the divisibility rule of 15 apply to all integers?
6.How can children in United Kingdom use numbers in everyday life to understand Divisibility Rule of 15?
7.What are some fun ways kids in United Kingdom can practice Divisibility Rule of 15 with numbers?
8.What role do numbers and Divisibility Rule of 15 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Divisibility Rule of 15 skills?
Important Glossaries for Divisibility Rule of 15
- Divisibility rule: A method used to determine whether one number is divisible by another without performing actual division.
- Multiples: Numbers obtained by multiplying a given number by an integer. For example, multiples of 15 are 15, 30, 45, 60, etc.
- Integers: Whole numbers that include positive numbers, negative numbers, and zero.
- Sum of digits: The total obtained by adding all the digits of a number together.
- Divisible: A number is divisible by another if, after division, the remainder is 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.
