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106 LearnersLast updated on September 24, 2025
GCF of 3 and 48
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 to schedule events. In this topic, we will learn about the GCF of 3 and 48.
What is the GCF of 3 and 48?
The greatest common factor of 3 and 48 is 3. The largest divisor of two or more numbers is called the GCF of the numbers.
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 3 and 48?
To find the GCF of 3 and 48, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 3 and 48 by Using Listing of Factors
Steps to find the GCF of 3 and 48 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 3 = 1, 3. 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 3 and 48: 1, 3.
Step 3: Choose the largest factor The largest factor that both numbers have is 3. The GCF of 3 and 48 is 3.
GCF of 3 and 48 Using Prime Factorization
To find the GCF of 3 and 48 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 3: 3 = 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 factor is: 3
Step 3: Multiply the common prime factors 3 = 3 The Greatest Common Factor of 3 and 48 is 3.
GCF of 3 and 48 Using Division Method or Euclidean Algorithm Method
Find the GCF of 3 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 3 48 ÷ 3 = 16 (quotient), remainder = 48 - (3 x 16) = 0
The remainder is zero, so the divisor will become the GCF. The GCF of 3 and 48 is 3.
Common Mistakes and How to Avoid Them in GCF of 3 and 48
Finding the GCF of 3 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 48, 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 shows an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse 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 3 and 48 Examples
Problem 1
A gardener has 3 small pots and 48 large pots. She wants to arrange them in equal rows with the same number of pots in each row. How many pots will be in each row?
We should find the GCF of 3 and 48 GCF of 3 and 48 3 There will be 3 pots in each row.
Explanation
As the GCF of 3 and 48 is 3, the gardener can arrange the pots in 3 rows.
Each row will contain 1 small pot and 16 large pots.
Problem 2
A chef has 3 kilograms of sugar and 48 kilograms of flour. She wants to divide them into the largest possible equal portions for baking. How much will each portion weigh?
GCF of 3 and 48 3 Each portion will weigh 3 kilograms.
Explanation
There are 3 kilograms of sugar and 48 kilograms of flour.
To find the weight of each portion, we should find the GCF of 3 and 48.
Each portion will weigh 3 kilograms.
Problem 3
A painter has 3 liters of red paint and 48 liters of blue paint. She wants to mix them into the largest equal batches. What should be the size of each batch?
For calculating the largest equal batch size, we have to calculate the GCF of 3 and 48. The GCF of 3 and 48 3 The size of each batch is 3 liters.
Explanation
To calculate the largest batch size, first, we need to calculate the GCF of 3 and 48, which is 3.
The size of each batch will be 3 liters.
Problem 4
A seamstress has two pieces of fabric, one 3 meters long and the other 48 meters long. She wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?
The seamstress needs the longest piece of fabric GCF of 3 and 48 3 The longest length of each piece is 3 meters.
Explanation
To find the longest length of each piece of the two fabrics, 3 meters and 48 meters respectively.
We have to find the GCF of 3 and 48, which is 3 meters.
The longest length of each piece is 3 meters.
Problem 5
If the GCF of 3 and ‘b’ is 3, and the LCM is 48, find ‘b’.
The value of ‘b’ is 48.
Explanation
GCF x LCM = product of the numbers
3 × 48 = 3 × b
144 = 3b
b = 144 ÷ 3
= 48
FAQs on the Greatest Common Factor of 3 and 48
1.What is the LCM of 3 and 48?
2.Is 3 a prime number?
3.What will be the GCF of any two consecutive numbers?
4.What is the prime factorization of 48?
5.Are 3 and 48 co-prime numbers?
Important Glossaries for GCF of 3 and 48
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.
- Prime Numbers: Numbers that have exactly two distinct positive divisors: 1 and the number itself. For example, 3 is a prime number.
- Prime Factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 12 is 22 x 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.
- LCM: The smallest common multiple of two or more numbers. For example, the LCM of 3 and 4 is 12.
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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.
