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

You are watching: What is the gcf of 12 and 18

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

Answer: GCF of 12 and 18 is 6.

Explanation:

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

Let's look in ~ the different methods because that finding the GCF of 12 and also 18.

Long division MethodPrime administrate MethodListing usual Factors

### GCF that 12 and also 18 by long Division

GCF of 12 and also 18 is the divisor that we obtain when the remainder i do not care 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 matching divisor (6) is the GCF the 12 and 18.

### GCF that 12 and also 18 by element Factorization

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

### GCF of 12 and 18 by Listing typical Factors

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

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

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## GCF that 12 and 18 Examples

Example 1: find the GCF of 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: find the greatest number the divides 12 and also 18 exactly.

Solution:

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

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

Therefore, the GCF of 12 and 18 is 6.

Example 3: For two numbers, GCF = 6 and also LCM = 36. If one number is 12, find the 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 top top GCF of 12 and 18

### What is the GCF the 12 and 18?

The GCF of 12 and also 18 is 6. To calculation the GCF (Greatest typical Factor) the 12 and 18, we need to aspect each number (factors the 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 also 18, i.e., 6.

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

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

### How to uncover the GCF the 12 and also 18 through Long department Method?

To uncover the GCF the 12, 18 utilizing long division method, 18 is split by 12. The equivalent divisor (6) as soon as remainder equals 0 is taken together GCF.

### What space the techniques to find GCF of 12 and also 18?

There are three generally used approaches to find the GCF the 12 and also 18.

See more: What Is A Property Of A Base S, Properties Of Acids And Bases

By prime FactorizationBy Euclidean AlgorithmBy lengthy Division

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

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

### If the GCF that 18 and 12 is 6, find 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