# GCF of 8 and 6

Created by: Team Maths - Examples.com, Last Updated: May 29, 2024

## GCF of 8 and 6

To find the Greatest Common Factor (GCF) of 8 and 6, list the factors of each numbers: the factors of 8 are 1, 2, 4, and 8, while the factors of 6 are 1, 2, 3, and 6. The common factors are 1 and 2, with the greatest common factor being 2. Therefore, the GCF of 8 and 6 is 2.

## Methods to Find GCF of 8 and 6

1. Prime Factorization Method
2. Long Division Method
3. Listing Common Factors

## GCF of 8 and 6 by Prime Factorization Method.

To find the Greatest Common Factor (GCF) of 8 and 6 using the prime factorization method, follow these steps:

### Step 1: Find the prime factorization of each number

Prime factorization of 8:

8 = 2 × 2 × 2 = 2³

Prime factorization of 6:

6 = 2 × 3

### Step 2: Identify the common prime factors

The common prime factor of 8 and 6 is 2.

### Step 3: Multiply the common prime factors

Since the only common prime factor is 2, the GCF is 2.

## GCF of 8 and 6 by Long Division Method.

To find the Greatest Common Factor (GCF) of 8 and 6 using the long division method, follow these steps:

### Step 1: Divide the larger number by the smaller number

8 ÷ 6 = 1 with a remainder of 2.

### Step 2: Replace the larger number with the smaller number, and the smaller number with the remainder

Now, we have 6 and 2.

### Step 3: Repeat the division

6 ÷ 2 = 3 with a remainder of 0.

### Step 4: When the remainder is 0, the divisors is the GCF

The last non-zero remainder is 2. So, the GCF of 8 and 6 is 2.

## GCF of 8 and 6 by Listing Common Factors.

To find the Greatest Common Factor (GCF) of 8 and 6 by listing common factors, follow these steps:

Factors of 8:

• 1, 2, 4, 8

Factors of 6:

• 1, 2, 3, 6

### Step 2: Identify the common factors

Common factors of 8 and 6:

• 1, 2

### Step 3: Determine the greatest common factor

The largest common factor is 2. Therefore, the GCF of 8 and 6 is 2.

## How are the GCF and LCM of two numbers related?

The product of the GCF and LCM of two numbers equals the product of the numbers.

## Can the GCF of two numbers ever be one of the numbers?

Yes, if one number is a multiple of the other. For example, the GCF of 2 and 6 is 2.

## Can the GCF of 8 and 6 be used to simplify the fraction 8/6?

Yes, simplifying 8/6 using the GCF of 2 gives 4/3.

## Can the GCF of 8 and 6 be greater than 2?

No, 2 is the greatest common factor of 8 and 6.

## How do you find the GCF of 8 and 6?

You can find the GCF by using methods such as listing common factors, prime factorization, and the long division method.

## How do you explain the GCF to someone learning it for the first time?

Describe it as the largest number that can divide two or more numbers without leaving a remainder. For 8 and 6, that number is 2.

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