GCF of 8 and 12

Find the Greatest Common Factor (GCF) of 8 and 12 with a complete step-by-step solution. The GCF is the largest number that divides both numbers without leaving a remainder.

Answer: GCF(8, 12) = 4

Step-by-Step Solution

Step 1 Find the Factors of 8

To find the GCF of 8 and 12, we first need to find all factors of each number.

The factors of 8 are numbers that divide 8 evenly:

1 × 8 = 8, 2 × 4 = 8

Factors of 8: 1, 2, 4, 8

Step 2 Find the Factors of 12

Now we find all factors of 12:

1 × 12 = 12, 2 × 6 = 12, 3 × 4 = 12

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

Step 3 Find the Common Factors

The common factors are numbers that appear in both lists:

Factors of 8: 1, 2, 4, 8

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

Common factors: 1, 2, 4

The Greatest Common Factor is the largest of these: 4

Step 4 Prime Factorization Method

We can also find the GCF using prime factorization:

8 = 2^3

12 = 2^2 × 3

Take the common prime factors with the lowest powers:

GCF = 2 × 2 = 4

Step 5 Euclidean Algorithm

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

12 = 1 × 8 + 4

8 = 2 × 4 + 0

When the remainder is 0, the GCF is the last divisor: 4

Step 6 Final Answer

GCF(8, 12) = 4

GCF of 8 and 12

Related Calculations