103 LearnersLast updated on August 5th, 2025
GCF of 18 and 15
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 18 and 15.
What is the GCF of 18 and 15?
The greatest common factor of 18 and 15 is 3. The largest divisor of two or more numbers is called the GCF of the numbers. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 18 and 15?
To find the GCF of 18 and 15, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 18 and 15 by Using Listing of Factors
Steps to find the GCF of 18 and 15 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 18 = 1, 2, 3, 6, 9, 18.
Factors of 15 = 1, 3, 5, 15.
Step 2: Now, identify the common factors of them Common factors of 18 and 15: 1, 3.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 3.
The GCF of 18 and 15 is 3.
GCF of 18 and 15 Using Prime Factorization
To find the GCF of 18 and 15 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 18: 18 = 2 × 3 × 3 = 2 × 3²
Prime Factors of 15: 15 = 3 × 5
Step 2: Now, identify the common prime factors. The common prime factor is: 3
Step 3: Multiply the common prime factors. The Greatest Common Factor of 18 and 15 is 3.
GCF of 18 and 15 Using Division Method or Euclidean Algorithm Method
Find the GCF of 18 and 15 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 18 by 15 18 ÷ 15 = 1 (quotient),
The remainder is calculated as 18 − (15×1) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (15) by the previous remainder (3)
Divide 15 by 3 15 ÷ 3 = 5 (quotient), remainder = 15 − (3×5) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 18 and 15 is 3.
Common Mistakes and How to Avoid Them in GCF of 18 and 15
Finding the GCF of 18 and 15 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 18, students may mention 8, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 18 and 15 Examples
Problem 1
A baker has 18 chocolate cookies and 15 vanilla cookies. She wants to package them in equal sets, with the largest number of cookies in each set. How many cookies will be in each set?
We should find the GCF of 18 and 15 GCF of 18 and 15 3
There are 3 equal sets
18 ÷ 3 = 6
15 ÷ 3 = 5
There will be 3 sets, and each set gets 6 chocolate cookies and 5 vanilla cookies.
Explanation
As the GCF of 18 and 15 is 3, the baker can make 3 sets.
Now divide 18 and 15 by 3.
Each set gets 6 chocolate cookies and 5 vanilla cookies.
Problem 2
A workshop has 18 hammers and 15 screwdrivers. They want to organize them in toolkits with the same number of tools in each toolkit, using the largest possible number of tools per toolkit. How many tools will be in each toolkit?
GCF of 18 and 15 3. So each toolkit will have 3 tools.
Explanation
There are 18 hammers and 15 screwdrivers.
To find the total number of tools in each toolkit, we should find the GCF of 18 and 15.
There will be 3 tools in each toolkit.
Problem 3
A florist has 18 tulips and 15 roses. She wants to arrange them in bouquets of equal size, using the largest possible number of flowers per bouquet. What should be the size of each bouquet?
For calculating the largest equal size, we have to calculate the GCF of 18 and 15
The GCF of 18 and 15 3
The bouquet has 3 flowers.
Explanation
For calculating the largest size of the bouquet, first, we need to calculate the GCF of 18 and 15, which is 3. The size of each bouquet will be 3 flowers.
Problem 4
A gardener has two plots, one with 18 sunflower plants and the other with 15 marigold plants. He wants to divide them into the longest possible equal rows, without any plants left over. What should be the length of each row?
The gardener needs the longest row of plants GCF of 18 and 15 3 .The longest length of each row is 3 plants.
Explanation
To find the longest length of each row of the two plots, 18 sunflower plants and 15 marigold plants, respectively, we have to find the GCF of 18 and 15, which is 3 plants. The longest length of each row is 3 plants.
Problem 5
If the GCF of 18 and ‘b’ is 3, and the LCM is 90. Find ‘b’.
The value of ‘b’ is 30.
Explanation
GCF × LCM = product of the numbers
3 × 90 = 18 × b
270 = 18b
b = 270 ÷ 18 = 15
FAQs on the Greatest Common Factor of 18 and 15
1.What is the LCM of 18 and 15?
2.Is 18 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 15?
5.Are 18 and 15 prime numbers?
6.How can children in United Kingdom use numbers in everyday life to understand GCF of 18 and 15?
7.What are some fun ways kids in United Kingdom can practice GCF of 18 and 15 with numbers?
8.What role do numbers and GCF of 18 and 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 GCF of 18 and 15 skills?
Important Glossaries for GCF of 18 and 15
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 12 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 17 is divided by 5, the remainder is 2, and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 18 and 15 is 90.
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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.
