GCF of 48 and 42
2026-02-28 10:58 Diff
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Last updated on August 5, 2025

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.

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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.

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?

Okay, lets begin

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.

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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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

If the GCF of 48 and ‘b’ is 6, and the LCM is 336. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 42.

Explanation

GCF × LCM = product of the numbers

6 × 336 = 48 × b

2016 = 48b

b = 2016 ÷ 48 = 42

Well explained 👍

FAQs on the Greatest Common Factor of 48 and 42

1.What is the LCM of 48 and 42?

The LCM of 48 and 42 is 336.

2.Is 48 divisible by 3?

Yes, 48 is divisible by 3 because the sum of its digits (4 + 8 = 12) is divisible by 3.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 42?

The prime factorization of 42 is 2 × 3 × 7.

5.Are 48 and 42 prime numbers?

No, 48 and 42 are not prime numbers because both of them have more than two factors.

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.

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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.