GCF of 6 and 8

Find the Greatest Common Factor (GCF) of 6 and 8 with a complete step-by-step solution. The GCF is the largest number that divides both numbers without leaving a remainder.

Answer: GCF(6, 8) = 2

Step-by-Step Solution

Step 1 Find the Factors of 6

To find the GCF of 6 and 8, we first need to find all factors of each number.

The factors of 6 are numbers that divide 6 evenly:

1 × 6 = 6, 2 × 3 = 6

Factors of 6: 1, 2, 3, 6

Step 2 Find the Factors of 8

Now we find all factors of 8:

1 × 8 = 8, 2 × 4 = 8

Factors of 8: 1, 2, 4, 8

Step 3 Find the Common Factors

The common factors are numbers that appear in both lists:

Factors of 6: 1, 2, 3, 6

Factors of 8: 1, 2, 4, 8

Common factors: 1, 2

The Greatest Common Factor is the largest of these: 2

Step 4 Prime Factorization Method

We can also find the GCF using prime factorization:

6 = 2 × 3

8 = 2^3

Take the common prime factors with the lowest powers:

GCF = 2 = 2

Step 5 Euclidean Algorithm

The Euclidean algorithm is a fast way to find the GCF using repeated division:

8 = 1 × 6 + 2

6 = 3 × 2 + 0

When the remainder is 0, the GCF is the last divisor: 2

Step 6 Final Answer

GCF(6, 8) = 2

GCF of 6 and 8

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