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104 LearnersLast updated on September 24, 2025
GCF of 12, 18, and 24
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 12, 18, and 24.
What is the GCF of 12, 18, and 24?
The greatest common factor of 12, 18, and 24 is 6. The largest divisor of two or more numbers is called the GCF of the numbers.
If numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of numbers cannot be negative because divisors are always positive.
How to find the GCF of 12, 18, and 24?
To find the GCF of 12, 18, and 24, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 12, 18, and 24 by Using Listing of Factors
Steps to find the GCF of 12, 18, and 24 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 12 = 1, 2, 3, 4, 6, 12. Factors of 18 = 1, 2, 3, 6, 9, 18. Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Step 2: Now, identify the common factors of them Common factors of 12, 18, and 24: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that all numbers have is 6. The GCF of 12, 18, and 24 is 6.
GCF of 12, 18, and 24 Using Prime Factorization
To find the GCF of 12, 18, and 24 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 12: 12 = 2 x 2 x 3 = 22 x 3 Prime Factors of 18: 18 = 2 x 3 x 3 = 2 x 32 Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 23 x 3
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 12, 18, and 24 is 6.
GCF of 12, 18, and 24 Using Division Method or Euclidean Algorithm Method
Find the GCF of 12, 18, and 24 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 24 by 18 24 ÷ 18 = 1 (quotient), The remainder is calculated as 24 − (18×1) = 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 12, 18, and 24 is 6.
Common Mistakes and How to Avoid Them in GCF of 12, 18, and 24
Finding the GCF of 12, 18, and 24 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 5, 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 indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse 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 12, 18, and 24 Examples
Problem 1
A baker has 12 chocolate muffins, 18 vanilla muffins, and 24 strawberry muffins. She wants to group them into boxes with the same number of muffins, using the largest number of muffins per box. How many muffins will be in each box?
We should find the GCF of 12, 18, and 24 GCF of 12, 18, and 24 2 x 3 = 6. There are 6 equal groups 12 ÷ 6 = 2 18 ÷ 6 = 3 24 ÷ 6 = 4 There will be 6 groups, and each group gets 2 chocolate, 3 vanilla, and 4 strawberry muffins.
Explanation
As the GCF of 12, 18, and 24 is 6, the baker can make 6 groups.
Now divide 12, 18, and 24 by 6.
Each group gets 2 chocolate, 3 vanilla, and 4 strawberry muffins.
Problem 2
A florist has 12 red roses, 18 white lilies, and 24 yellow tulips. She wants to arrange them in bouquets with the same number of flowers, using the largest possible number of flowers per bouquet. How many flowers will be in each bouquet?
GCF of 12, 18, and 24 2 x 3 = 6. So each bouquet will have 6 flowers.
Explanation
There are 12 red roses, 18 white lilies, and 24 yellow tulips.
To find the total number of flowers in each bouquet, we should find the GCF of 12, 18, and 24.
There will be 6 flowers in each bouquet.
Problem 3
A gardener has 12 meters of red fencing, 18 meters of green fencing, and 24 meters of blue fencing. She wants to cut all the fencing into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 12, 18, and 24 The GCF of 12, 18, and 24 2 x 3 = 6. The fencing is 6 meters long.
Explanation
For calculating the longest length of the fencing, first, we need to calculate the GCF of 12, 18, and 24, which is 6.
The length of each piece of fencing will be 6 meters.
Problem 4
A chef has two pieces of cheese, one 12 cm long and the other 18 cm long, and a piece of chocolate 24 cm long. He wants to cut them into the longest possible equal pieces, without any leftovers. What should be the length of each piece?
The chef needs the longest piece of cheese and chocolate GCF of 12, 18, and 24 2 x 3 = 6. The longest length of each piece is 6 cm.
Explanation
To find the longest length of each piece of cheese and chocolate, 12 cm, 18 cm, and 24 cm, respectively.
We have to find the GCF of 12, 18, and 24, which is 6 cm.
The longest length of each piece is 6 cm.
Problem 5
If the GCF of 12 and ‘b’ is 6, and the LCM is 36, find ‘b’.
The value of ‘b’ is 18.
Explanation
GCF x LCM = product of the numbers
6 × 36 = 12 × b
216 = 12b
b = 216 ÷ 12
= 18
FAQs on the Greatest Common Factor of 12, 18, and 24
1.What is the LCM of 12, 18, and 24?
2.Is 18 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 24?
5.Are 12, 18, and 24 prime numbers?
Important Glossaries for GCF of 12, 18, and 24
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Prime Factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 18 is 2 x 3^2.
- Common Factors: Numbers that are factors of two or more numbers. For example, the common factors of 12, 18, and 24 are 1, 2, 3, and 6.
- Greatest Common Factor (GCF): The largest factor that commonly divides two or more numbers. For example, the GCF of 12, 18, and 24 is 6.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 25 is divided by 4, the remainder is 1.
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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.
