Summarize this article:
103 LearnersLast updated on September 18, 2025
GCF of 24 and 48
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 24 and 48.
What is the GCF of 24 and 48?
The greatest common factor of 24 and 48 is 24. 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 48?
To find the GCF of 24 and 48, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 24 and 48 by Using Listing of Factors
Steps to find the GCF of 24 and 48 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 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Step 2: Now, identify the common factors Common factors of 24 and 48: 1, 2, 3, 4, 6, 8, 12, 24.
Step 3: Choose the largest factor The largest factor that both numbers have is 24. The GCF of 24 and 48 is 24.
GCF of 24 and 48 Using Prime Factorization
To find the GCF of 24 and 48 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 48: 48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 x 3 = 2³ x 3
Step 3: Multiply the common prime factors 2³ x 3 = 8 x 3 = 24. The Greatest Common Factor of 24 and 48 is 24.
GCF of 24 and 48 Using Division Method or Euclidean Algorithm Method
Find the GCF of 24 and 48 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 48 by 24 48 ÷ 24 = 2 (quotient), The remainder is calculated as 48 − (24 x 2) = 0 Since the remainder is zero, the divisor is the GCF.
The GCF of 24 and 48 is 24.
Common Mistakes and How to Avoid Them in GCF of 24 and 48
Finding the GCF of 24 and 48 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 indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with 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 24 and 48 Examples
Problem 1
A chef has 24 apples and 48 oranges. He wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 24 and 48 GCF of 24 and 48 2³ x 3 = 8 x 3 = 24.
There are 24 equal groups 24 ÷ 24 = 1 48 ÷ 24 = 2
There will be 24 groups, and each group gets 1 apple and 2 oranges.
Explanation
As the GCF of 24 and 48 is 24, the chef can make 24 groups.
Now, divide 24 and 48 by 24.
Each group gets 1 apple and 2 oranges.
Problem 2
A factory has 24 red widgets and 48 blue widgets. They want to arrange them in boxes with the same number of widgets in each box, using the largest possible number of widgets per box. How many widgets will be in each box?
GCF of 24 and 48 2³ x 3 = 8 x 3 = 24. So each box will have 24 widgets.
Explanation
There are 24 red and 48 blue widgets.
To find the total number of widgets in each box, we should find the GCF of 24 and 48.
There will be 24 widgets in each box.
Problem 3
A gardener has 24 meters of red hose and 48 meters of blue hose. She wants to cut both hoses 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 48
The GCF of 24 and 48 2³ x 3 = 8 x 3 = 24.
The hose is 24 meters long.
Explanation
For calculating the longest length of the hose, first, we need to calculate the GCF of 24 and 48, which is 24.
The length of each piece of the hose will be 24 meters.
Problem 4
A carpenter has two wooden planks, one 24 cm long and the other 48 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 48 2³ x 3 = 8 x 3 = 24.
The longest length of each piece is 24 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 24 cm and 48 cm, respectively, we have to find the GCF of 24 and 48, which is 24 cm.
The longest length of each piece is 24 cm.
Problem 5
If the GCF of 24 and ‘a’ is 24, and the LCM is 48, find ‘a’.
The value of ‘a’ is 48.
Explanation
GCF x LCM = product of the numbers
24 x 48 = 24 x a
1152 = 24a
a = 1152 ÷ 24 = 48
FAQs on the Greatest Common Factor of 24 and 48
1.What is the LCM of 24 and 48?
2.Is 24 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 48?
5.Are 24 and 48 prime numbers?
Important Glossaries for GCF of 24 and 48
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 6 are 6, 12, 18, 24, 30, 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 24 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 24 and 48 is 48.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 24 and 48
![Important Math Links Icon]()
Next to GCF of 24 and 48
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.
