GCF the 12 and 18 is the largest possible number the divides 12 and also 18 exactly without any remainder. The determinants of 12 and also 18 room 1, 2, 3, 4, 6, 12 and 1, 2, 3, 6, 9, 18 respectively. There space 3 generally used approaches to discover the GCF the 12 and also 18 - prime factorization, long division, and also Euclidean algorithm.

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

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

Answer: GCF of 12 and 18 is 6.

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Explanation:

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


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

Long department MethodPrime administer MethodListing usual Factors

GCF that 12 and 18 by long Division

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

Step 2: since 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 18.

GCF of 12 and also 18 by prime Factorization

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

GCF of 12 and also 18 by Listing common Factors

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

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

☛ also Check:


GCF of 12 and 18 Examples


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

Solution:

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


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

Solution:

The best number the divides 12 and also 18 specifically is their greatest usual factor, i.e. GCF the 12 and 18.⇒ components of 12 and 18:

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

Therefore, the GCF the 12 and 18 is 6.


Example 3: For 2 numbers, GCF = 6 and also LCM = 36. If one number is 12, uncover 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 other number is 18.


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FAQs top top GCF that 12 and 18

What is the GCF of 12 and also 18?

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

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

The complying with equation deserve to be supplied to refer the relation in between LCM and also GCF that 12 and 18, i.e. GCF × LCM = 12 × 18.

How to find the GCF that 12 and also 18 through Long department Method?

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

What space the methods to find GCF the 12 and also 18?

There are three commonly used methods to discover the GCF of 12 and also 18.

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By element FactorizationBy Euclidean AlgorithmBy long Division

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

To find the GCF the 12 and also 18, us will uncover the prime factorization of the provided numbers, i.e. 12 = 2 × 2 × 3; 18 = 2 × 3 × 3.⇒ because 2, 3 are typical terms in the element factorization the 12 and also 18. Hence, GCF(12, 18) = 2 × 3 = 6☛ What room Prime Numbers?

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

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