GCF of 24 and 42
2026-02-28 00:49 Diff
https://brightchamps.com/en-us/math/numbers/gcf-of-24-and-42

198 Learners

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 24 and 42.

What is the GCF of 24 and 42?

The greatest common factor of 24 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, which are always positive.

How to find the GCF of 24 and 42?

To find the GCF of 24 and 42, a few methods are described below:

  • Listing Factors
     
  • Prime Factorization
     
  • Long Division Method / by Euclidean Algorithm

GCF of 24 and 42 by Using Listing of Factors

Steps to find the GCF of 24 and 42 using the listing of factors:

Step 1: Firstly, list the factors of each number

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.

Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42.

Step 2: Now, identify the common factors of them Common factors of 24 and 42: 1, 2, 3, 6.

Step 3: Choose the largest factor The largest factor that both numbers have is 6.

The GCF of 24 and 42 is 6.

Explore Our Programs

GCF of 24 and 42 Using Prime Factorization

To find the GCF of 24 and 42 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 24: 24 = 2 × 2 × 2 × 3 = 2³ × 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 24 and 42 is 6.

GCF of 24 and 42 Using Division Method or Euclidean Algorithm Method

Find the GCF of 24 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 42 by 24 42 ÷ 24 = 1 (quotient),

The remainder is calculated as 42 − (24×1) = 18

The remainder is 18, not zero, so continue the process

Step 2: Now divide the previous divisor (24) by the previous remainder (18)

Divide 24 by 18 24 ÷ 18 = 1 (quotient), remainder = 24 − (18×1) = 6

Step 3: Now divide the previous divisor (18) by the previous remainder (6) 18 ÷ 6 = 3 (quotient), remainder = 18 − (6×3) = 0

The remainder is zero, the divisor will become the GCF.

The GCF of 24 and 42 is 6.

Common Mistakes and How to Avoid Them in GCF of 24 and 42

Finding GCF of 24 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 chef has 24 apples and 42 oranges. She wants to arrange them in fruit baskets with the same number of fruits in each basket. How many fruits will be in each basket?

Okay, lets begin

We should find the GCF of 24 and 42 GCF of 24 and 42

2 × 3 = 6.

There are 6 fruits per basket.

24 ÷ 6 = 4

42 ÷ 6 = 7

There will be 6 baskets, and each basket gets 4 apples and 7 oranges.

Explanation

As the GCF of 24 and 42 is 6, the chef can make 6 baskets.

Now divide 24 and 42 by 6.

Each basket gets 4 apples and 7 oranges.

Well explained 👍

Problem 2

A gardener has 24 rose bushes and 42 tulip plants. She 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?

Okay, lets begin

GCF of 24 and 42 2 × 3 = 6. So each row will have 6 plants.

Explanation

There are 24 rose bushes and 42 tulip plants.

To find the total number of plants in each row, we should find the GCF of 24 and 42.

There will be 6 plants in each row.

Well explained 👍

Problem 3

A baker has 24 chocolate cookies and 42 vanilla cookies. He wants to pack them into boxes with equal quantities, using the largest possible number of cookies per box. How many cookies should be in each box?

Okay, lets begin

For calculating the largest equal number of cookies per box, we have to calculate the GCF of 24 and 42

The GCF of 24 and 42

2 × 3 = 6.

There will be 6 cookies per box.

Explanation

For calculating the largest number of cookies per box, first, we need to calculate the GCF of 24 and 42, which is 6. The number of cookies in each box will be 6.

Well explained 👍

Problem 4

A carpenter has two wooden beams, one 24 cm long and the other 42 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?

Okay, lets begin

The carpenter needs the longest piece of wood GCF of 24 and 42

2 × 3 = 6.

The longest length of each piece is 6 cm.

Explanation

To find the longest length of each piece of the two wooden beams, 24 cm and 42 cm, respectively, we have to find the GCF of 24 and 42, which is 6 cm.

The longest length of each piece is 6 cm.

Well explained 👍

Problem 5

If the GCF of 24 and ‘b’ is 6, and the LCM is 168, find ‘b’.

Okay, lets begin

The value of ‘b’ is 42.

Explanation

GCF × LCM = product of the numbers

6 × 168 = 24 × b

1008 = 24b

b = 1008 ÷ 24 = 42

Well explained 👍

FAQs on the Greatest Common Factor of 24 and 42

1.What is the LCM of 24 and 42?

The LCM of 24 and 42 is 168.

2.Is 24 divisible by 2?

Yes, 24 is divisible by 2 because it is an even number.

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 24 and 42 prime numbers?

No, 24 and 42 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 24 and 42

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 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 14 are 2 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 24 and 42 is 168.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.