101 LearnersLast updated on July 31st, 2025
GCF of 48 and 42
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 42.
What is the GCF of 48 and 42?
The greatest common factor of 48 and 42 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 48 and 42?
To find the GCF of 48 and 42, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 48 and 42 by Using Listing of factors
Steps to find the GCF of 48 and 42 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 42 = 1, 2, 3, 6, 7, 14, 21, 42.
Step 2: Now, identify the common factors of them. Common factors of 48 and 42: 1, 2, 3, 6.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 6.
The GCF of 48 and 42 is 6.
GCF of 48 and 42 Using Prime Factorization
To find the GCF of 48 and 42 using the 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 = 2⁴ × 3
Prime Factors of 42: 42 = 2 × 3 × 7
Step 2: Now, identify the common prime factors. The common prime factors are: 2 × 3
Step 3: Multiply the common prime factors 2 × 3 = 6.
The Greatest Common Factor of 48 and 42 is 6.
GCF of 48 and 42 Using Division Method or Euclidean Algorithm Method
Find the GCF of 48 and 42 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 42 48 ÷ 42 = 1 (quotient), The remainder is calculated as 48 − (42 × 1) = 6
The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (42) by the previous remainder (6)
Divide 42 by 6 42 ÷ 6 = 7 (quotient), remainder = 42 − (6 × 7) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 48 and 42 is 6.
Common Mistakes and How to Avoid Them in GCF of 48 and 42
Finding GCF of 48 and 42 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 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 42 Examples
Problem 1
A gardener has 48 tulips and 42 roses. She wants to plant them in flower beds with the greatest number of the same type of flower in each bed. How many flowers will be in each bed?
We should find the GCF of 48 and 42. GCF of 48 and 42
2 × 3 = 6.
There are 6 flowers in each bed.
48 ÷ 6 = 8
42 ÷ 6 = 7
There will be 6 beds, and each bed gets 8 tulips and 7 roses.
Explanation
As the GCF of 48 and 42 is 6, the gardener can make 6 beds.
Now divide 48 and 42 by 6.
Each bed gets 8 tulips and 7 roses.
Problem 2
A chef has 48 ounces of sugar and 42 ounces of flour. They want to divide them into containers with the same amount of each ingredient in each container, using the largest possible amount. How many ounces will be in each container?
GCF of 48 and 42 2 × 3 = 6. So each container will have 6 ounces.
Explanation
There are 48 ounces of sugar and 42 ounces of flour.
To find the total number of ounces in each container, we should find the GCF of 48 and 42.
There will be 6 ounces in each container.
Problem 3
A builder has 48 feet of wooden planks and 42 feet of metal rods. He wants to cut them 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 42.
The GCF of 48 and 42
2 × 3 = 6.
The pieces are 6 feet long.
Explanation
For calculating the longest length of the pieces first, we need to calculate the GCF of 48 and 42, which is 6. The length of each piece will be 6 feet.
Problem 4
A decorator has two rolls of fabric, one 48 meters long and the other 42 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 decorator needs the longest piece of fabric. GCF of 48 and 42
2 × 3 = 6.
The longest length of each piece is 6 meters.
Explanation
To find the longest length of each piece of the two rolls of fabric, 48 meters and 42 meters, respectively, we have to find the GCF of 48 and 42, which is 6 meters. The longest length of each piece is 6 meters.
Problem 5
If the GCF of 48 and ‘b’ is 6, and the LCM is 336. Find ‘b’.
The value of ‘b’ is 42.
Explanation
GCF × LCM = product of the numbers
6 × 336 = 48 × b
2016 = 48b
b = 2016 ÷ 48 = 42
FAQs on the Greatest Common Factor of 48 and 42
1.What is the LCM of 48 and 42?
2.Is 48 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 42?
5.Are 48 and 42 prime numbers?
6.How can children in Vietnam use numbers in everyday life to understand GCF of 48 and 42?
7.What are some fun ways kids in Vietnam can practice GCF of 48 and 42 with numbers?
8.What role do numbers and GCF of 48 and 42 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve GCF of 48 and 42 skills?
Important Glossaries for GCF of 48 and 42
- 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 42 are 2, 3, and 7.
- 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 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 48 and 42 is 336.
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.
