GCF that 12 and 18 is the largest feasible number the divides 12 and 18 specifically without any type of remainder. The factors of 12 and also 18 room 1, 2, 3, 4, 6, 12 and also 1, 2, 3, 6, 9, 18 respectively. There space 3 commonly used techniques to uncover the GCF the 12 and also 18 - prime factorization, long division, and also Euclidean algorithm.

You are watching: The greatest common factor of 12 and 18

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

Answer: GCF the 12 and 18 is 6.

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Explanation:

The GCF of 2 non-zero integers, x(12) and also y(18), is the greatest positive integer m(6) that divides both x(12) and y(18) without any kind of remainder.


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

Long department MethodPrime administer MethodListing typical Factors

GCF of 12 and also 18 by lengthy Division

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GCF of 12 and also 18 is the divisor the we get when the remainder i do not care 0 after doing long division repeatedly.

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

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

GCF of 12 and also 18 by prime Factorization

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

GCF that 12 and 18 by Listing usual Factors

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Factors the 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 are 1, 2, 3, and also 6. Therefore, the greatest common factor the 12 and 18 is 6.

☛ also Check:


GCF that 12 and also 18 Examples


Example 1: uncover the GCF the 12 and 18, if their LCM is 36.

Solution:

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


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

Solution:

The best number the divides 12 and also 18 specifically is your greatest common factor, i.e. GCF that 12 and also 18.⇒ factors of 12 and 18:

Factors the 12 = 1, 2, 3, 4, 6, 12Factors the 18 = 1, 2, 3, 6, 9, 18

Therefore, the GCF the 12 and 18 is 6.


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

Solution:

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


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FAQs top top GCF the 12 and also 18

What is the GCF that 12 and 18?

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

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

The following equation have the right to be provided to refer the relation in between LCM and GCF that 12 and also 18, i.e. GCF × LCM = 12 × 18.

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

To find the GCF that 12, 18 using long department method, 18 is divided by 12. The corresponding divisor (6) as soon as remainder equals 0 is taken together GCF.

What space the techniques to uncover GCF that 12 and 18?

There are three generally used techniques to uncover the GCF that 12 and also 18.

See more: What Is The Density Of Coke Have More Mass Than Diet Coke? Density Of Coke

By element FactorizationBy Euclidean AlgorithmBy long Division

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

To find the GCF the 12 and 18, us will find the element factorization that the provided 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 that 12 and also 18. Hence, GCF(12, 18) = 2 × 3 = 6☛ What are Prime Numbers?

If the GCF of 18 and 12 is 6, uncover its LCM.

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