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What Is The Greatest Common Factor Of 18 And 12, What Is The Greatest Common Factor Of 12 And 18

GCF of 12 and 18 is the largest possible number that divides 12 and 18 exactly without any remainder. The factors of 12 and 18 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 6, 9, 18 respectively. There are 3 commonly used methods to find the GCF of 12 and 18 – prime factorization, long division, and Euclidean algorithm.

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

Answer: GCF of 12 and 18 is 6.

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Explanation:

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

Let's look at the different methods for finding the GCF of 12 and 18.

Long Division MethodPrime Factorization MethodListing Common Factors

GCF of 12 and 18 by Long Division

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

Step 2: Since the remainder ≠ 0, we will 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.

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GCF of 12 and 18 by Prime Factorization

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

GCF of 12 and 18 by Listing Common Factors

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

There are 4 common factors of 12 and 18, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 12 and 18 is 6.

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GCF of 12 and 18 Examples

Example 1: Find the GCF of 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 18 is 6.

Example 2: Find the greatest number that divides 12 and 18 exactly.

Solution:

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

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

Therefore, the GCF of 12 and 18 is 6.

Example 3: For two numbers, GCF = 6 and 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 on GCF of 12 and 18

What is the GCF of 12 and 18?

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

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

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

How to Find the GCF of 12 and 18 by Long Division Method?

To find the GCF of 12, 18 using long division method, 18 is divided by 12. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 12 and 18?

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

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By Prime FactorizationBy Euclidean AlgorithmBy Long Division

How to Find the GCF of 12 and 18 by Prime Factorization?

To find the GCF of 12 and 18, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 18 = 2 × 3 × 3.⇒ Since 2, 3 are common terms in the prime factorization of 12 and 18. Hence, GCF(12, 18) = 2 × 3 = 6☛ What are Prime Numbers?

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

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

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