GCF of 12 and 24 is the largest possible number that divides 12 and 24 exactly without any remainder. The factors of 12 and 24 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the GCF of 12 and 24 - Euclidean algorithm, long division, and prime factorization.

You are watching: Find the greatest common factor of 12 and 24

1.GCF of 12 and 24
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 12 and 24 is 12.

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Explanation:

The GCF of two non-zero integers, x(12) and y(24), is the greatest positive integer m(12) that divides both x(12) and y(24) without any remainder.


The methods to find the GCF of 12 and 24 are explained below.

Long Division MethodPrime Factorization MethodListing Common Factors

GCF of 12 and 24 by Long Division

GCF of 12 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 2: Since the remainder = 0, the divisor (12) is the GCF of 12 and 24.

The corresponding divisor (12) is the GCF of 12 and 24.

GCF of 12 and 24 by Prime Factorization

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Prime factorization of 12 and 24 is (2 × 2 × 3) and (2 × 2 × 2 × 3) respectively. As visible, 12 and 24 have common prime factors. Hence, the GCF of 12 and 24 is 2 × 2 × 3 = 12.

GCF of 12 and 24 by Listing Common Factors

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Factors of 12: 1, 2, 3, 4, 6, 12Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

There are 6 common factors of 12 and 24, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 12 and 24 is 12.

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GCF of 12 and 24 Examples


Example 1: Find the GCF of 12 and 24, if their LCM is 24.

Solution:

∵ LCM × GCF = 12 × 24⇒ GCF(12, 24) = (12 × 24)/24 = 12Therefore, the greatest common factor of 12 and 24 is 12.


Example 2: For two numbers, GCF = 12 and LCM = 24. If one number is 12, find the other number.

Solution:

Given: GCF (z, 12) = 12 and LCM (z, 12) = 24∵ GCF × LCM = 12 × (z)⇒ z = (GCF × LCM)/12⇒ z = (12 × 24)/12⇒ z = 24Therefore, the other number is 24.


Example 3: The product of two numbers is 288. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 288∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 288/12Therefore, the LCM is 24.


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FAQs on GCF of 12 and 24

What is the GCF of 12 and 24?

The GCF of 12 and 24 is 12. To calculate the greatest common factor of 12 and 24, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the greatest factor that exactly divides both 12 and 24, i.e., 12.

What is the Relation Between LCM and GCF of 12, 24?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 12 and 24, i.e. GCF × LCM = 12 × 24.

If the GCF of 24 and 12 is 12, Find its LCM.

GCF(24, 12) × LCM(24, 12) = 24 × 12Since the GCF of 24 and 12 = 12⇒ 12 × LCM(24, 12) = 288Therefore, LCM = 24☛ GCF Calculator

What are the Methods to Find GCF of 12 and 24?

There are three commonly used methods to find the GCF of 12 and 24.

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By Euclidean AlgorithmBy Prime FactorizationBy Long Division

How to Find the GCF of 12 and 24 by Long Division Method?

To find the GCF of 12, 24 using long division method, 24 is divided by 12. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

How to Find the GCF of 12 and 24 by Prime Factorization?

To find the GCF of 12 and 24, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 24 = 2 × 2 × 2 × 3.⇒ Since 2, 2, 3 are common terms in the prime factorization of 12 and 24. Hence, GCF(12, 24) = 2 × 2 × 3 = 12☛ What are Prime Numbers?