GCF of 12 and 24
2026-02-28 08:56 Diff
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Last updated on August 12, 2025

The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 12 and 24.

What is the GCF of 12 and 24?

The greatest common factor of 12 and 24 is 12. 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 12 and 24?

To find the GCF of 12 and 24, a few methods are described below -

  1. Listing Factors
  2. Prime Factorization
  3. Long Division Method / by Euclidean Algorithm

GCF of 12 and 24 by Using Listing of Factors

Steps to find the GCF of 12 and 24 using the listing of factors

Step 1: Firstly, list the factors of each number

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

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

Step 2: Now, identify the common factors of them Common factors of 12 and 24: 1, 2, 3, 4, 6, 12.

Step 3: Choose the largest factor The largest factor that both numbers have is 12.

The GCF of 12 and 24 is 12.

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GCF of 12 and 24 Using Prime Factorization

To find the GCF of 12 and 24 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 12: 12 = 2 × 2 × 3 = 2² × 3

Prime Factors of 24: 24 = 2 × 2 × 2 × 3 = 2³ × 3

Step 2: Now, identify the common prime factors The common prime factors are: 2 × 2 × 3 = 2² × 3

Step 3: Multiply the common prime factors 2² × 3 = 4 × 3 = 12.

The Greatest Common Factor of 12 and 24 is 12.

GCF of 12 and 24 Using Division Method or Euclidean Algorithm Method

Find the GCF of 12 and 24 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 24 by 12 24 ÷ 12 = 2 (quotient), remainder = 24 − (12×2) = 0

The remainder is zero, so the divisor becomes the GCF. The GCF of 12 and 24 is 12.

Common Mistakes and How to Avoid Them in GCF of 12 and 24

Finding the GCF of 12 and 24 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.

Problem 1

A baker has 12 loaves of bread and 24 muffins. He wants to package them into equal sets, with the largest number of items in each set. How many items will be in each set?

Okay, lets begin

We should find the GCF of 12 and 24. GCF of 12 and 24: 2² × 3 = 4 × 3 = 12. There are 12 equal sets. 12 ÷ 12 = 1 24 ÷ 12 = 2 There will be 12 sets, and each set gets 1 loaf of bread and 2 muffins.

Explanation

As the GCF of 12 and 24 is 12, the baker can make 12 sets. Now divide 12 and 24 by 12. Each set gets 1 loaf of bread and 2 muffins.

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Problem 2

A gardener has 12 roses and 24 tulips. They want to plant them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?

Okay, lets begin

GCF of 12 and 24: 2² × 3 = 4 × 3 = 12. So, each row will have 12 flowers.

Explanation

There are 12 roses and 24 tulips. To find the total number of flowers in each row, we should find the GCF of 12 and 24. There will be 12 flowers in each row.

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Problem 3

A tailor has 12 meters of white fabric and 24 meters of blue fabric. She wants to cut both fabrics 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 12 and 24. The GCF of 12 and 24: 2² × 3 = 4 × 3 = 12. Each piece of fabric is 12 meters long.

Explanation

For calculating the longest length of the fabric, first, we need to calculate the GCF of 12 and 24, which is 12. The length of each piece of fabric will be 12 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 12 cm long and the other 24 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 12 and 24: 2² × 3 = 4 × 3 = 12. The longest length of each piece is 12 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 12 cm and 24 cm respectively, we have to find the GCF of 12 and 24, which is 12 cm. The longest length of each piece is 12 cm.

Well explained 👍

Problem 5

If the GCF of 12 and ‘b’ is 12, and the LCM is 48, find ‘b’.

Okay, lets begin

The value of ‘b’ is 24.

Explanation

GCF × LCM = product of the numbers 12 × 48 = 12 × b 576 = 12b b = 576 ÷ 12 = 48

Well explained 👍

FAQs on the Greatest Common Factor of 12 and 24

1.What is the LCM of 12 and 24?

The LCM of 12 and 24 is 24.

2.Is 12 divisible by 3?

Yes, 12 is divisible by 3 because 12 divided by 3 gives an integer value of 4.

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 24?

The prime factorization of 24 is 2³ × 3.

5.Are 12 and 24 prime numbers?

No, 12 and 24 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 12 and 24

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
  • 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 24 are 2 and 3.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 24 is 24.

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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.