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103 LearnersLast updated on September 9, 2025
GCF of 48 and 60
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 60.
What is the GCF of 48 and 60?
The greatest common factor of 48 and 60 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 48 and 60?
To find the GCF of 48 and 60, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 48 and 60 by Using Listing of factors
Steps to find the GCF of 48 and 60 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 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 48 and 60: 1, 2, 3, 4, 6, 12.
Step 3: Choose the largest factor The largest factor that both numbers have is 12. The GCF of 48 and 60 is 12.
GCF of 48 and 60 Using Prime Factorization
To find the GCF of 48 and 60 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 48: 48 = 2 × 2 × 2 × 2 × 3 = 2^4 × 3 Prime Factors of 60: 60 = 2 × 2 × 3 × 5 = 2^2 × 3 × 5
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 2 × 3 = 2^2 × 3
Step 3: Multiply the common prime factors 2^2 × 3 = 4 × 3 = 12. The Greatest Common Factor of 48 and 60 is 12.
GCF of 48 and 60 Using Division Method or Euclidean Algorithm Method
Find the GCF of 48 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 48 60 ÷ 48 = 1 (quotient), The remainder is calculated as 60 − (48 × 1) = 12 The remainder is 12, not zero, so continue the process
Step 2: Now divide the previous divisor (48) by the previous remainder (12) Divide 48 by 12 48 ÷ 12 = 4 (quotient), remainder = 48 − (12 × 4) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 48 and 60 is 12.
Common Mistakes and How to Avoid Them in GCF of 48 and 60
Finding GCF of 48 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
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 48, students may mention 9 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 48 and 60 Examples
Problem 1
A farmer has 48 apple trees and 60 orange trees. He wants to organize them into the largest possible equal groups. How many trees will be in each group?
We should find GCF of 48 and 60 GCF of 48 and 60 2^2 × 3 = 4 × 3 = 12. There are 12 equal groups 48 ÷ 12 = 4 60 ÷ 12 = 5 There will be 12 groups, and each group gets 4 apple trees and 5 orange trees.
Explanation
As the GCF of 48 and 60 is 12, the farmer can make 12 groups.
Now divide 48 and 60 by 12.
Each group gets 4 apple trees and 5 orange trees.
Problem 2
A company has 48 laptops and 60 tablets. They want to distribute them in rows with the same number of devices in each row, using the largest possible number of devices per row. How many devices will be in each row?
GCF of 48 and 60 2^2 × 3 = 4 × 3 = 12. So each row will have 12 devices.
Explanation
There are 48 laptops and 60 tablets.
To find the total number of devices in each row, we should find the GCF of 48 and 60.
There will be 12 devices in each row.
Problem 3
A chef has 48 kg of flour and 60 kg of sugar. She wants to divide both into bags of equal weight, using the heaviest possible weight for each bag. What should be the weight of each bag?
For calculating the heaviest equal weight, we have to calculate the GCF of 48 and 60 The GCF of 48 and 60 2^2 × 3 = 4 × 3 = 12. Each bag will weigh 12 kg.
Explanation
For calculating the heaviest weight for the bags first we need to calculate the GCF of 48 and 60 which is 12.
The weight of each bag will be 12 kg.
Problem 4
A contractor has two metal rods, one 48 cm long and the other 60 cm long. He wants to cut them into the longest possible equal pieces, without any metal left over. What should be the length of each piece?
The contractor needs the longest piece of metal GCF of 48 and 60 2^2 × 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 metal rods, 48 cm and 60 cm, respectively.
We have to find the GCF of 48 and 60, which is 12 cm.
The longest length of each piece is 12 cm.
Problem 5
If the GCF of 48 and ‘b’ is 12, and the LCM is 240. Find ‘b’.
The value of ‘b’ is 60.
Explanation
GCF × LCM = product of the numbers
12 × 240
= 48 × b
2880 = 48b b
= 2880 ÷ 48 = 60
FAQs on the Greatest Common Factor of 48 and 60
1.What is the LCM of 48 and 60?
2.Is 48 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 60?
5.Are 48 and 60 prime numbers?
Important Glossaries for GCF of 48 and 60
- 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 48 and 60 is 240.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 50 and 60 will be 10, 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.
