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

You are watching: What is the gcf of 12 and 24

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

Answer: GCF that 12 and also 24 is 12.

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Explanation:

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


The approaches to discover the GCF of 12 and 24 are described below.

Long division MethodPrime administer MethodListing typical Factors

GCF the 12 and 24 by long Division

GCF the 12 and also 24 is the divisor the we obtain when the remainder i do not care 0 after ~ doing long division repeatedly.

Step 2: due to the fact that the remainder = 0, the divisor (12) is the GCF the 12 and 24.

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

GCF that 12 and 24 by element Factorization

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

GCF the 12 and 24 by Listing typical Factors

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

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

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GCF of 12 and 24 Examples


Example 1: uncover the GCF that 12 and also 24, if your LCM is 24.

Solution:

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


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

Solution:

Given: GCF (z, 12) = 12 and also 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 your LCM?

Solution:

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


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FAQs top top GCF the 12 and also 24

What is the GCF of 12 and 24?

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

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

The following equation deserve to be provided to express the relation between LCM (Least usual Multiple) and also GCF the 12 and 24, i.e. GCF × LCM = 12 × 24.

If the GCF of 24 and also 12 is 12, uncover 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 approaches to uncover GCF that 12 and also 24?

There room three commonly used techniques to uncover the GCF that 12 and also 24.

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By Euclidean AlgorithmBy prime FactorizationBy lengthy Division

How to discover the GCF of 12 and 24 by Long department Method?

To find the GCF that 12, 24 utilizing long department method, 24 is divided by 12. The corresponding divisor (12) once remainder equates to 0 is taken as GCF.

How to find the GCF of 12 and 24 by prime Factorization?

To find the GCF that 12 and also 24, we will find the element factorization of the offered numbers, i.e. 12 = 2 × 2 × 3; 24 = 2 × 2 × 2 × 3.⇒ due to the fact that 2, 2, 3 are common terms in the element factorization that 12 and 24. Hence, GCF(12, 24) = 2 × 2 × 3 = 12☛ What space Prime Numbers?