GCF the 12 and also 18 is the largest possible number that divides 12 and also 18 precisely without any kind of remainder. The determinants of 12 and 18 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 6, 9, 18 respectively. There space 3 typically used techniques to uncover the GCF that 12 and also 18 - prime factorization, long division, and also Euclidean algorithm.

You are watching: What is the greatest common factor of 18 and 12

1.GCF the 12 and 18
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF that 12 and 18 is 6.

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Explanation:

The GCF of two non-zero integers, x(12) and also y(18), is the greatest positive essence m(6) that divides both x(12) and also y(18) without any type of remainder.


Let's look at the various methods because that finding the GCF that 12 and also 18.

Long department MethodPrime factorization MethodListing common Factors

GCF the 12 and 18 by long Division

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GCF the 12 and 18 is the divisor the we get when the remainder becomes 0 after ~ doing long division repeatedly.

Step 2: because the remainder ≠ 0, we will certainly divide the divisor of step 1 (12) by the remainder (6).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the GCF of 12 and also 18.

GCF of 12 and 18 by element Factorization

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Prime factorization of 12 and also 18 is (2 × 2 × 3) and also (2 × 3 × 3) respectively. Together visible, 12 and also 18 have common prime factors. Hence, the GCF of 12 and also 18 is 2 × 3 = 6.

GCF of 12 and 18 by Listing typical Factors

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Factors that 12: 1, 2, 3, 4, 6, 12Factors of 18: 1, 2, 3, 6, 9, 18

There space 4 usual factors the 12 and also 18, that space 1, 2, 3, and 6. Therefore, the greatest typical factor that 12 and 18 is 6.

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GCF the 12 and 18 Examples


Example 1: discover the GCF the 12 and also 18, if your LCM is 36.

Solution:

∵ LCM × GCF = 12 × 18⇒ GCF(12, 18) = (12 × 18)/36 = 6Therefore, the greatest typical factor the 12 and also 18 is 6.


Example 2: find the best number that divides 12 and also 18 exactly.

Solution:

The biggest number that divides 12 and also 18 exactly is their greatest common factor, i.e. GCF that 12 and 18.⇒ determinants of 12 and 18:

Factors that 12 = 1, 2, 3, 4, 6, 12Factors of 18 = 1, 2, 3, 6, 9, 18

Therefore, the GCF that 12 and also 18 is 6.


Example 3: For two numbers, GCF = 6 and also LCM = 36. If one number is 12, discover the various other number.

Solution:

Given: GCF (x, 12) = 6 and LCM (x, 12) = 36∵ GCF × LCM = 12 × (x)⇒ x = (GCF × LCM)/12⇒ x = (6 × 36)/12⇒ x = 18Therefore, the other number is 18.


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FAQs ~ above GCF the 12 and 18

What is the GCF that 12 and also 18?

The GCF that 12 and 18 is 6. To calculation the GCF (Greatest typical Factor) of 12 and 18, we require to element each number (factors of 12 = 1, 2, 3, 4, 6, 12; determinants of 18 = 1, 2, 3, 6, 9, 18) and also choose the greatest element that exactly divides both 12 and 18, i.e., 6.

What is the Relation in between LCM and GCF of 12, 18?

The following equation can be provided to to express the relation between LCM and GCF of 12 and also 18, i.e. GCF × LCM = 12 × 18.

How to uncover the GCF the 12 and 18 by Long division Method?

To find the GCF the 12, 18 utilizing long department method, 18 is separated by 12. The corresponding divisor (6) when remainder amounts to 0 is taken as GCF.

What room the approaches to find GCF the 12 and 18?

There are three commonly used approaches to find the GCF of 12 and 18.

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By element FactorizationBy Euclidean AlgorithmBy long Division

How to uncover the GCF the 12 and also 18 by prime Factorization?

To discover the GCF the 12 and 18, us will discover the prime factorization that the given numbers, i.e. 12 = 2 × 2 × 3; 18 = 2 × 3 × 3.⇒ due to the fact that 2, 3 are usual terms in the element factorization of 12 and 18. Hence, GCF(12, 18) = 2 × 3 = 6☛ What are Prime Numbers?

If the GCF that 18 and also 12 is 6, discover its LCM.

GCF(18, 12) × LCM(18, 12) = 18 × 12Since the GCF that 18 and also 12 = 6⇒ 6 × LCM(18, 12) = 216Therefore, LCM = 36☛ GCF Calculator