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104 LearnersLast updated on September 24, 2025
GCF of 48 and 120
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 48 and 120.
What is the GCF of 48 and 120?
The greatest common factor of 48 and 120 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 48 and 120?
To find the GCF of 48 and 120, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 48 and 120 by Using Listing of factors
Steps to find the GCF of 48 and 120 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
Step 2: Now, identify the common factors of them Common factors of 48 and 120: 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 48 and 120 is 24.
GCF of 48 and 120 Using Prime Factorization
To find the GCF of 48 and 120 using Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number
Prime Factors of 48: 48 = 2 x 2 x 2 x 2 x 3 = 24 x 3
Prime Factors of 120: 120 = 2 x 2 x 2 x 3 x 5 = 23 x 3 x 5
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 48 and 120 is 24.
GCF of 48 and 120 Using Division Method or Euclidean Algorithm Method
Find the GCF of 48 and 120 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 120 by 48 120 ÷ 48 = 2 (quotient), The remainder is calculated as 120 − (48×2) = 24 The remainder is 24, not zero, so continue the process
Step 2: Now divide the previous divisor (48) by the previous remainder (24) Divide 48 by 24 48 ÷ 24 = 2 (quotient), remainder = 48 − (24×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 48 and 120 is 24.
Common Mistakes and How to Avoid Them in GCF of 48 and 120
Finding GCF of 48 and 120 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 48, students may mention 50, 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; 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 48 and 120 Examples
Problem 1
A park has 48 trees and 120 flower pots. The park manager wants to arrange them into groups with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 48 and 120 GCF of 48 and 120 23 x 3 = 8 x 3 = 24.
There are 24 equal groups 48 ÷ 24 = 2 120 ÷ 24 = 5
There will be 24 groups, and each group gets 2 trees and 5 flower pots.
Explanation
As the GCF of 48 and 120 is 24, the park manager can make 24 groups.
Now divide 48 and 120 by 24. Each group gets 2 trees and 5 flower pots.
Problem 2
A company has 48 laptops and 120 tablets. They want to distribute them in sets with the same number of devices in each set, using the largest possible number of devices per set. How many devices will be in each set?
GCF of 48 and 120 2^3 x 3 = 8 x 3 = 24.
So each set will have 24 devices.
Explanation
There are 48 laptops and 120 tablets.
To find the total number of devices in each set, we should find the GCF of 48 and 120. There will be 24 devices in each set.
Problem 3
A factory has 48 meters of wire and 120 meters of cable. The manager wants to cut both 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 48 and 120
The GCF of 48 and 120 23 x 3 = 8 x 3 = 24.
The length of each piece is 24 meters.
Explanation
For calculating the longest length of the wire and cable first we need to calculate the GCF of 48 and 120 which is 24. The length of each piece will be 24 meters.
Problem 4
A chef has two rolls of dough, one 48 cm long and the other 120 cm 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 chef needs the longest piece of dough GCF of 48 and 120 2^3 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 rolls of dough, 48 cm and 120 cm, respectively.
We have to find the GCF of 48 and 120, which is 24 cm.
The longest length of each piece is 24 cm.
Problem 5
If the GCF of 48 and ‘b’ is 24, and the LCM is 240, find ‘b’.
The value of ‘b’ is 120.
Explanation
GCF x LCM = product of the numbers
24 × 240 = 48 × b
5760 = 48b
b = 5760 ÷ 48 = 120
FAQs on the Greatest Common Factor of 48 and 120
1.What is the LCM of 48 and 120?
2.Is 48 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 120?
5.Are 48 and 120 prime numbers?
Important Glossaries for GCF of 48 and 120
- 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.
- 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 48 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 48 and 120 is 240.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 48 and 120 is 24, as it is their largest common factor that divides the numbers completely.
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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.
