Last updated on July 30th, 2025
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.
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.
To find the GCF of 18 and 15, a few methods are described below:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If the GCF of 18 and ‘b’ is 3, and the LCM is 90. Find ‘b’.
The value of ‘b’ is 30.
GCF × LCM = product of the numbers
3 × 90 = 18 × b
270 = 18b
b = 270 ÷ 18 = 15
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.
: She loves to read number jokes and games.