GCF the 6 and 12 is the largest possible number that divides 6 and also 12 exactly without any type of remainder. The components of 6 and also 12 room 1, 2, 3, 6 and 1, 2, 3, 4, 6, 12 respectively. There are 3 frequently used techniques to uncover the GCF the 6 and 12 - lengthy division, Euclidean algorithm, and also prime factorization.

You are watching: What is the greatest common factor of 6 and 12

1.GCF of 6 and 12
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 6 and also 12 is 6.

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Explanation:

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


The methods to discover the GCF that 6 and also 12 are described below.

Long department MethodPrime administrate MethodListing typical Factors

GCF that 6 and also 12 by lengthy Division

GCF of 6 and 12 is the divisor that we get when the remainder i do not care 0 ~ doing long division repeatedly.

Step 2: since the remainder = 0, the divisor (6) is the GCF of 6 and also 12.

The equivalent divisor (6) is the GCF the 6 and 12.

GCF of 6 and also 12 by prime Factorization

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

GCF of 6 and also 12 by Listing typical Factors

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

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

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GCF that 6 and also 12 Examples


Example 1: find the GCF of 6 and 12, if your LCM is 12.

Solution:

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


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

Solution:

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


Example 3: The product of 2 numbers is 72. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and also product of number = 72∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 72/6Therefore, the LCM is 12.


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FAQs on GCF that 6 and also 12

What is the GCF that 6 and 12?

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

What is the Relation between LCM and also GCF that 6, 12?

The complying with equation can be offered to to express the relation between LCM and also GCF the 6 and 12, i.e. GCF × LCM = 6 × 12.

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

GCF(12, 6) × LCM(12, 6) = 12 × 6Since the GCF of 12 and also 6 = 6⇒ 6 × LCM(12, 6) = 72Therefore, LCM = 12☛ GCF Calculator

What room the approaches to uncover GCF the 6 and also 12?

There space three commonly used approaches to find the GCF the 6 and 12.

See more: How Many Sides Does A Circle Have A Face S Does A Circle Have

By Listing typical FactorsBy element FactorizationBy lengthy Division

How to find the GCF the 6 and 12 by Long department Method?

To discover the GCF the 6, 12 using long division method, 12 is separated by 6. The matching divisor (6) as soon as remainder amounts to 0 is taken together GCF.

How to uncover the GCF that 6 and 12 by prime Factorization?

To uncover the GCF of 6 and also 12, us will discover the element factorization that the provided numbers, i.e. 6 = 2 × 3; 12 = 2 × 2 × 3.⇒ due to the fact that 2, 3 are typical terms in the prime factorization that 6 and also 12. Hence, GCF(6, 12) = 2 × 3 = 6☛ What is a prime Number?