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105 LearnersLast updated on October 7, 2025
GCF of 24 and 108
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 24 and 108.
What is the GCF of 24 and 108?
The greatest common factor of 24 and 108 is 12.
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 24 and 108?
To find the GCF of 24 and 108, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 24 and 108 by Using Listing of factors
Steps to find the GCF of 24 and 108 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24. Factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
Step 2: Now, identify the common factors of them Common factors of 24 and 108: 1, 2, 3, 4, 6, 12.
Step 3: Choose the largest factor The largest factor that both numbers have is 12.
The GCF of 24 and 108 is 12.
GCF of 24 and 108 Using Prime Factorization
To find the GCF of 24 and 108 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 2³ x 3 Prime Factors of 108: 108 = 2 x 2 x 3 x 3 x 3 = 2² x 3³.
Step 2: Now, identify the common prime factors, The common prime factors are: 2 x 2 x 3 = 2² x 3.
Step 3: Multiply the common prime factors 2² x 3 = 4 × 3 = 12.
The Greatest Common Factor of 24 and 108 is 12.
GCF of 24 and 108 Using Division Method or Euclidean Algorithm Method
Find the GCF of 24 and 108 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 108 by 24 108 ÷ 24 = 4 (quotient), The remainder is calculated as 108 − (24×4) = 12. The remainder is 12, not zero, so continue the process.
Step 2: Now divide the previous divisor (24) by the previous remainder (12) Divide 24 by 12 24 ÷ 12 = 2 (quotient), remainder = 24 − (12×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 24 and 108 is 12.
Common Mistakes and How to Avoid Them in GCF of 24 and 108
Finding GCF of 24 and 108 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 24, students may mention 10 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 GCF of two numbers will always be an even number.
But it's not true that 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 24 and 108 Examples
Problem 1
A gardener has 24 tulip bulbs and 108 daffodil bulbs. She wants to plant them in identical rows, with the largest number of bulbs in each row. How many bulbs will be in each row?
We should find GCF of 24 and 108 GCF of 24 and 108 2² x 3 = 4 x 3 = 12.
There are 12 bulbs in each row. 24 ÷ 12 = 2 108 ÷ 12 = 9.
There will be 12 bulbs in each row, with 2 tulips and 9 daffodils.
Explanation
As the GCF of 24 and 108 is 12, the gardener can plant 12 bulbs in each row.
Now divide 24 and 108 by 12.
Each row gets 2 tulips and 9 daffodils.
Problem 2
A baker has 24 chocolate cookies and 108 vanilla cookies. She wants to pack them into boxes with the same number of cookies in each box, using the largest possible number of cookies per box. How many cookies will be in each box?
GCF of 24 and 108 2² x 3 = 4 × 3 = 12.
So each box will have 12 cookies.
Explanation
There are 24 chocolate and 108 vanilla cookies.
To find the total number of cookies in each box, we should find the GCF of 24 and 108.
There will be 12 cookies in each box.
Problem 3
A tailor has 24 meters of red fabric and 108 meters of blue fabric. She wants to cut both fabrics 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 24 and 108.
The GCF of 24 and 108 2² x 3 = 4 × 3 = 12.
Each piece of fabric is 12 meters long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 24 and 108, which is 12.
The length of each piece of the fabric will be 12 meters.
Problem 4
A carpenter has two wooden planks, one 24 cm long and the other 108 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 24 and 108 2² x 3 = 4 × 3 = 12.
The longest length of each piece is 12 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 24 cm and 108 cm, respectively, we have to find the GCF of 24 and 108, which is 12 cm.
The longest length of each piece is 12 cm.
Problem 5
If the GCF of 24 and ‘a’ is 12, and the LCM is 216, find ‘a’.
The value of ‘a’ is 108.
Explanation
GCF x LCM = product of the numbers 12 × 216 = 24 × a 2592 = 24a a = 2592 ÷ 24 = 108
FAQs on the Greatest Common Factor of 24 and 108
1.What is the LCM of 24 and 108?
2.Is 108 divisible by 6?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 108?
5.Are 24 and 108 prime numbers?
Important Glossaries for GCF of 24 and 108
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, 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 15 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 24 and 36 is 72.
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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.
