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107 LearnersLast updated on October 3, 2025
GCF of 48 and 96
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 96.
What is the GCF of 48 and 96?
The greatest common factor of 48 and 96 is 48.
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 96?
To find the GCF of 48 and 96, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 48 and 96 by Using Listing of Factors
Steps to find the GCF of 48 and 96 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 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.
Step 2: Now, identify the common factors of them Common factors of 48 and 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Step 3: Choose the largest factor, The largest factor that both numbers have is 48.
The GCF of 48 and 96 is 48.
GCF of 48 and 96 Using Prime Factorization
To find the GCF of 48 and 96 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 96: 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2^5 × 3.
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 2 × 2 × 2 × 3 = 2^4 × 3.
Step 3: Multiply the common prime factors 2^4 × 3 = 16 × 3 = 48.
The Greatest Common Factor of 48 and 96 is 48.
GCF of 48 and 96 Using Division Method or Euclidean Algorithm Method
Find the GCF of 48 and 96 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 96 by 48 96 ÷ 48 = 2 (quotient), The remainder is calculated as 96 - (48 × 2) = 0 Since the remainder is zero, the divisor will become the GCF.
The GCF of 48 and 96 is 48.
Common Mistakes and How to Avoid Them in GCF of 48 and 96
Finding GCF of 48 and 96 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 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 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 48 and 96 Examples
Problem 1
A gardener has 48 rose plants and 96 tulip plants. She wants to arrange them in rows with the maximum number of plants in each row. How many plants will be in each row?
We should find the GCF of 48 and 96 GCF of 48 and 96 2^4 × 3 = 16 × 3 = 48.
Each row will have 48 plants.
Explanation
As the GCF of 48 and 96 is 48, the gardener can arrange the plants in rows of 48.
Problem 2
A warehouse has 48 small boxes and 96 large boxes. They want to group them into stacks with the same number of boxes in each stack, using the largest possible number of boxes per stack. How many boxes will be in each stack?
GCF of 48 and 96 2^4 × 3 = 16 × 3 = 48.
So each stack will have 48 boxes.
Explanation
There are 48 small boxes and 96 large boxes.
To find the total number of boxes in each stack, we should find the GCF of 48 and 96.
Each stack will have 48 boxes.
Problem 3
A ribbon factory has 48 meters of red ribbon and 96 meters of blue ribbon. The manufacturer wants to cut both ribbons 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 96 The GCF of 48 and 96 2^4 × 3 = 16 × 3 = 48.
The ribbon is 48 meters long.
Explanation
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 48 and 96, which is 48.
The length of each piece of the ribbon will be 48 meters.
Problem 4
A carpenter has two wooden planks, one 48 cm long and the other 96 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 48 and 96 2^4 × 3 = 16 × 3 = 48.
The longest length of each piece is 48 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 48 cm and 96 cm, respectively, we have to find the GCF of 48 and 96, which is 48 cm.
The longest length of each piece is 48 cm.
Problem 5
If the GCF of 48 and ‘b’ is 48, and the LCM is 96. Find ‘b’.
The value of ‘b’ is 96.
Explanation
GCF × LCM = product of the numbers 48 × 96 = 48 × b 4608 = 48b b = 4608 ÷ 48 = 96
FAQs on the Greatest Common Factor of 48 and 96
1.What is the LCM of 48 and 96?
2.Is 48 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 96?
5.Are 48 and 96 prime numbers?
Important Glossaries for GCF of 48 and 96
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
- 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 48 are 2 and 3.
- 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 96 is 96.
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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.
