GCF the 6 and 8 is the largest feasible number that divides 6 and 8 exactly without any kind of remainder. The components of 6 and 8 room 1, 2, 3, 6 and 1, 2, 4, 8 respectively. There are 3 frequently used methods to uncover the GCF the 6 and 8 - element factorization, Euclidean algorithm, and long division.

You are watching: What is the gcf of 6 and 8

1.GCF the 6 and 8
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 6 and also 8 is 2.

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Explanation:

The GCF of two non-zero integers, x(6) and also y(8), is the greatest positive integer m(2) the divides both x(6) and y(8) without any type of remainder.


Let's look at the various methods because that finding the GCF that 6 and 8.

Prime administer MethodListing usual FactorsLong department Method

GCF of 6 and 8 by prime Factorization

Prime administrate of 6 and 8 is (2 × 3) and (2 × 2 × 2) respectively. Together visible, 6 and 8 have only one typical prime factor i.e. 2. Hence, the GCF of 6 and also 8 is 2.

GCF of 6 and also 8 by Listing typical Factors

Factors that 6: 1, 2, 3, 6Factors of 8: 1, 2, 4, 8

There space 2 usual factors that 6 and 8, that room 1 and 2. Therefore, the greatest typical factor that 6 and also 8 is 2.

GCF of 6 and 8 by long Division

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GCF the 6 and 8 is the divisor the we obtain when the remainder becomes 0 ~ doing long division repeatedly.

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

The matching divisor (2) is the GCF that 6 and 8.

☛ additionally Check:


GCF the 6 and 8 Examples


Example 1: find the GCF the 6 and also 8, if their LCM is 24.

Solution:

∵ LCM × GCF = 6 × 8⇒ GCF(6, 8) = (6 × 8)/24 = 2Therefore, the greatest typical factor the 6 and 8 is 2.


Example 2: For two numbers, GCF = 2 and LCM = 24. If one number is 8, uncover the various other number.

Solution:

Given: GCF (y, 8) = 2 and LCM (y, 8) = 24∵ GCF × LCM = 8 × (y)⇒ y = (GCF × LCM)/8⇒ y = (2 × 24)/8⇒ y = 6Therefore, the various other number is 6.


Example 3: discover the biggest number the divides 6 and 8 exactly.

Solution:

The greatest number the divides 6 and 8 exactly is their greatest typical factor, i.e. GCF of 6 and 8.⇒ components of 6 and also 8:

Factors the 6 = 1, 2, 3, 6Factors the 8 = 1, 2, 4, 8

Therefore, the GCF that 6 and 8 is 2.


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FAQs on GCF that 6 and 8

What is the GCF the 6 and also 8?

The GCF the 6 and also 8 is 2. To calculate the greatest usual factor (GCF) that 6 and also 8, we require to variable each number (factors the 6 = 1, 2, 3, 6; determinants of 8 = 1, 2, 4, 8) and choose the greatest variable that precisely divides both 6 and also 8, i.e., 2.

How to uncover the GCF the 6 and also 8 by prime Factorization?

To uncover the GCF of 6 and 8, us will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 8 = 2 × 2 × 2.⇒ because 2 is the only typical prime aspect of 6 and 8. Hence, GCF (6, 8) = 2.☛ What is a element Number?

What is the Relation between LCM and also GCF of 6, 8?

The adhering to equation have the right to be used to to express the relation between Least common Multiple (LCM) and also GCF that 6 and also 8, i.e. GCF × LCM = 6 × 8.

What room the methods to find GCF that 6 and 8?

There are three commonly used methods to find the GCF of 6 and 8.

By lengthy DivisionBy Listing common FactorsBy prime Factorization

If the GCF of 8 and also 6 is 2, discover its LCM.

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GCF(8, 6) × LCM(8, 6) = 8 × 6Since the GCF of 8 and also 6 = 2⇒ 2 × LCM(8, 6) = 48Therefore, LCM = 24☛ GCF Calculator

How to discover the GCF the 6 and also 8 by Long department Method?

To uncover the GCF that 6, 8 making use of long division method, 8 is separated by 6. The matching divisor (2) when remainder equates to 0 is taken together GCF.