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GCF of 6 and 8

GCF of 6 and 8 is the largest possible number that divides 6 and 8 exactly without any remainder. The factors of 6 and 8 are 1, 2, 3, 6 and 1, 2, 4, 8 respectively. There are 3 commonly used methods to find the GCF of 6 and 8 - prime factorization, Euclidean algorithm, and long division.

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

What is GCF of 6 and 8?

Answer: GCF of 6 and 8 is 2.

Explanation:

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

Methods to Find GCF of 6 and 8

Let's look at the different methods for finding the GCF of 6 and 8.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 6 and 8 by Prime Factorization

Prime factorization of 6 and 8 is (2 × 3) and (2 × 2 × 2) respectively. As visible, 6 and 8 have only one common prime factor i.e. 2. Hence, the GCF of 6 and 8 is 2.

GCF of 6 and 8 by Listing Common Factors

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

There are 2 common factors of 6 and 8, that are 1 and 2. Therefore, the greatest common factor of 6 and 8 is 2.

GCF of 6 and 8 by Long Division

GCF of 6 and 8 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 8 (larger number) by 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 6 and 8.

☛ Also Check:

GCF of 6 and 8 Examples

Example 1: Find the GCF of 6 and 8, if their LCM is 24.

Solution:

∵ LCM × GCF = 6 × 8
⇒ GCF(6, 8) = (6 × 8)/24 = 2
Therefore, the greatest common factor of 6 and 8 is 2.
Example 2: For two numbers, GCF = 2 and LCM = 24. If one number is 8, find the 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 = 6
Therefore, the other number is 6.
Example 3: Find the greatest number that divides 6 and 8 exactly.

Solution:

The greatest number that divides 6 and 8 exactly is their greatest common factor, i.e. GCF of 6 and 8.
⇒ Factors of 6 and 8:
- Factors of 6 = 1, 2, 3, 6
- Factors of 8 = 1, 2, 4, 8
Therefore, the GCF of 6 and 8 is 2.

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FAQs on GCF of 6 and 8

What is the GCF of 6 and 8?

The GCF of 6 and 8 is 2. To calculate the greatest common factor (GCF) of 6 and 8, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 8 = 1, 2, 4, 8) and choose the greatest factor that exactly divides both 6 and 8, i.e., 2.

How to Find the GCF of 6 and 8 by Prime Factorization?

To find the GCF of 6 and 8, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 8 = 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 6 and 8. Hence, GCF (6, 8) = 2.
☛ What is a Prime Number?

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

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 6 and 8, i.e. GCF × LCM = 6 × 8.

What are the Methods to Find GCF of 6 and 8?

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

By Long Division
By Listing Common Factors
By Prime Factorization

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

GCF(8, 6) × LCM(8, 6) = 8 × 6
Since the GCF of 8 and 6 = 2
⇒ 2 × LCM(8, 6) = 48
Therefore, LCM = 24
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How to Find the GCF of 6 and 8 by Long Division Method?

To find the GCF of 6, 8 using long division method, 8 is divided by 6. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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