102 LearnersLast updated on August 5th, 2025
GCF of 18 and 60
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 60.
What is the GCF of 18 and 60?
The greatest common factor of 18 and 60 is 6. The largest divisor of two or more numbers is called the GCF of the number. 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 60?
To find the GCF of 18 and 60, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 18 and 60 by Using Listing of factors
Steps to find the GCF of 18 and 60 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 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Step 2: Now, identify the common factors of them Common factors of 18 and 60: 1, 2, 3, 6.
Step 3: Choose the largest factor
The largest factor that both numbers have is 6.
The GCF of 18 and 60 is 6.
GCF of 18 and 60 Using Prime Factorization
To find the GCF of 18 and 60 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number
Prime Factors of 18: 18 = 2 x 3 x 3 = 2 x 3²
Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 2² x 3 x 5
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 3
Step 3: Multiply the common prime factors 2 x 3 = 6.
The Greatest Common Factor of 18 and 60 is 6.
GCF of 18 and 60 Using Division Method or Euclidean Algorithm Method
Find the GCF of 18 and 60 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 60 by 18 60 ÷ 18 = 3 (quotient),
The remainder is calculated as 60 − (18×3) = 6
The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (18) by the previous remainder (6)
Divide 18 by 6 18 ÷ 6 = 3 (quotient), remainder = 18 − (6×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 18 and 60 is 6.
Common Mistakes and How to Avoid Them in GCF of 18 and 60
Finding GCF of 18 and 60 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 between factors and 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 60 Examples
Problem 1
A gardener has 18 rose plants and 60 sunflower plants. She wants to plant them in rows with the largest possible number of plants in each row. How many plants will be in each row?
We should find the GCF of 18 and 60 GCF of 18 and 60 2 x 3 = 6.
There are 6 plants per row.
18 ÷ 6 = 3 60 ÷ 6 = 10
There will be 6 plants in each row, with 3 rows of rose plants and 10 rows of sunflower plants.
Explanation
As the GCF of 18 and 60 is 6, the gardener can make rows with 6 plants each. Now divide 18 and 60 by 6. Each row has 3 rose plants and 10 sunflower plants.
Problem 2
A chef has 18 apples and 60 oranges. He wants to make the largest possible number of fruit baskets with the same number of fruits in each basket. How many fruits will each basket contain?
GCF of 18 and 60 2 x 3 = 6.
So each basket will contain 6 fruits.
Explanation
There are 18 apples and 60 oranges. To find the total number of fruits in each basket, we should find the GCF of 18 and 60. Each basket will contain 6 fruits.
Problem 3
A coach has 18 soccer balls and 60 basketballs. He wants to divide them into groups with the largest possible number of balls per group. How many balls will each group contain?
For calculating the largest equal number of balls per group, we have to calculate the GCF of 18 and 60.
The GCF of 18 and 60 2 x 3 = 6.
Each group will contain 6 balls.
Explanation
To calculate the largest number of balls per group, first, we need to calculate the GCF of 18 and 60, which is 6. Each group will contain 6 balls.
Problem 4
A baker has two dough pieces, one 18 inches long and the other 60 inches long. He wants to cut them into the longest possible equal pieces, without any dough left over. What should be the length of each piece?
The baker needs the longest piece of dough GCF of 18 and 60 2 x 3 = 6.
The longest length of each piece is 6 inches.
Explanation
To find the longest length of each piece of the two dough pieces, 18 inches and 60 inches respectively, we have to find the GCF of 18 and 60, which is 6 inches. The longest length of each piece is 6 inches.
Problem 5
If the GCF of 18 and ‘b’ is 6, and the LCM is 180, find ‘b’.
The value of ‘b’ is 60.
Explanation
GCF x LCM = product of the numbers 6 × 180 = 18 × b
1080 = 18b
b = 1080 ÷ 18 = 60
FAQs on the Greatest Common Factor of 18 and 60
1.What is the LCM of 18 and 60?
2.Is 18 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 60?
5.Are 18 and 60 prime numbers?
6.How can children in Canada use numbers in everyday life to understand GCF of 18 and 60?
7.What are some fun ways kids in Canada can practice GCF of 18 and 60 with numbers?
8.What role do numbers and GCF of 18 and 60 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve GCF of 18 and 60 skills?
Important Glossaries for GCF of 18 and 60
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
- 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, 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 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 18 is divided by 7, the remainder is 4 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 18 and 60 is 180.
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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.
