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Last updated on August 5th, 2025

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GCF of 18 and 60

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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.

GCF of 18 and 60 for UAE Students
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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.

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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
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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.

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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.

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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.

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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

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Listing Incorrect Factors

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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

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Choosing the wrong common factor

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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

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Forgetting to include 1 as a factor

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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

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Using Multiples instead of factors

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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

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Assuming GCF is always an even number

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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.

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Greatest Common Factor of 18 and 60 Examples

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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?

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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.

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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?

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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.

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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?

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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.

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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?

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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.

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Problem 5

If the GCF of 18 and ‘b’ is 6, and the LCM is 180, find ‘b’.

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The value of ‘b’ is 60.

Explanation

GCF x LCM = product of the numbers 6 × 180 = 18 × b

1080 = 18b

b = 1080 ÷ 18 = 60

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FAQs on the Greatest Common Factor of 18 and 60

1.What is the LCM of 18 and 60?

The LCM of 18 and 60 is 180.

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2.Is 18 divisible by 2?

Yes, 18 is divisible by 2 because it is an even number.

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3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

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4.What is the prime factorization of 60?

The prime factorization of 60 is 2² x 3 x 5.

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5.Are 18 and 60 prime numbers?

No, 18 and 60 are not prime numbers because both of them have more than two factors.

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6.How can children in United Arab Emirates use numbers in everyday life to understand GCF of 18 and 60?

Numbers appear everywhere—from counting money to measuring ingredients. Kids in United Arab Emirates see how GCF of 18 and 60 helps solve real problems, making numbers meaningful beyond the classroom.

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7.What are some fun ways kids in United Arab Emirates can practice GCF of 18 and 60 with numbers?

Games like board games, sports scoring, or even cooking help children in United Arab Emirates use numbers naturally. These activities make practicing GCF of 18 and 60 enjoyable and connected to their world.

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8.What role do numbers and GCF of 18 and 60 play in helping children in United Arab Emirates develop problem-solving skills?

Working with numbers through GCF of 18 and 60 sharpens reasoning and critical thinking, preparing kids in United Arab Emirates for challenges inside and outside the classroom.

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9.How can families in United Arab Emirates create number-rich environments to improve GCF of 18 and 60 skills?

Families can include counting chores, measuring recipes, or budgeting allowances, helping children connect numbers and GCF of 18 and 60 with everyday activities.

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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.

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Fun Fact

: She loves to read number jokes and games.

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