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103 LearnersLast updated on September 23, 2025
GCF of 6 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 schedule events. In this topic, we will learn about the GCF of 6 and 48.
What is the GCF of 6 and 48?
The greatest common factor of 6 and 48 is 6. 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 6 and 48?
To find the GCF of 6 and 48, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 6 and 48 by Using Listing of Factors
Steps to find the GCF of 6 and 48 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 6 = 1, 2, 3, 6.
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Step 2: Now, identify the common factors of them Common factors of 6 and 48: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6. The GCF of 6 and 48 is 6.
GCF of 6 and 48 Using Prime Factorization
To find the GCF of 6 and 48 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 6: 6 = 2 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 3
Step 3: Multiply the common prime factors 2 x 3 = 6. The Greatest Common Factor of 6 and 48 is 6.
GCF of 6 and 48 Using Division Method or Euclidean Algorithm Method
Find the GCF of 6 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 6 48 ÷ 6 = 8 (quotient), The remainder is calculated as 48 - (6 x 8) = 0
The remainder is zero, so the divisor will become the GCF. The GCF of 6 and 48 is 6.
Common Mistakes and How to Avoid Them in GCF of 6 and 48
Finding the GCF of 6 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 6, 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 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 6 and 48 Examples
Problem 1
A chef has 6 kilograms of flour and 48 kilograms of sugar. She wants to divide them into equal portions, each containing the largest possible amount. How much of each will be in each portion?
We should find the GCF of 6 and 48 GCF of 6 and 48 2 x 3 = 6.
There are 6 equal portions 6 ÷ 6 = 1 kg of flour 48 ÷ 6 = 8 kg of sugar
Each portion will have 1 kg of flour and 8 kg of sugar.
Explanation
As the GCF of 6 and 48 is 6, the chef can make 6 portions. Now divide 6 and 48 by 6. Each portion will have 1 kg of flour and 8 kg of sugar.
Problem 2
A gardener has 6 rose bushes and 48 tulip bulbs. He wants to plant them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 6 and 48 2 x 3 = 6. So each row will have 6 plants.
Explanation
There are 6 rose bushes and 48 tulip bulbs. To find the total number of plants in each row, we should find the GCF of 6 and 48. There will be 6 plants in each row.
Problem 3
A teacher has 6 whiteboards and 48 markers. She wants to distribute them equally among classrooms, with the largest possible equal quantity. How many of each will each classroom receive?
For distributing equally, we have to calculate the GCF of 6 and 48 The GCF of 6 and 48 2 x 3 = 6.
Each classroom will receive 1 whiteboard and 8 markers.
Explanation
For distributing equally, first, we need to calculate the GCF of 6 and 48, which is 6. Each classroom will receive 1 whiteboard and 8 markers.
Problem 4
A painter has two canvases, one 6 meters long and the other 48 meters long. She wants to cut them into the longest possible equal pieces, without any canvas left over. What should be the length of each piece?
The painter needs the longest piece of canvas GCF of 6 and 48 2 x 3 = 6.
The longest length of each piece is 6 meters.
Explanation
To find the longest length of each piece of the two canvases, 6 meters and 48 meters, respectively, we have to find the GCF of 6 and 48, which is 6 meters.
The longest length of each piece is 6 meters.
Problem 5
If the GCF of 6 and 'b' is 6, and the LCM is 48, find 'b'.
The value of 'b' is 48.
Explanation
GCF x LCM = product of the numbers
6 x 48 = 6 x b
288 = 6b
b = 288 ÷ 6 = 48
FAQs on the Greatest Common Factor of 6 and 48
1.What is the LCM of 6 and 48?
2.Is 48 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 48?
5.Are 6 and 48 prime numbers?
Important Glossaries for GCF of 6 and 48
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.
- 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, 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 48 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 11 is divided by 5, the remainder is 1 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 6 and 48 is 48.
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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.
