GCF of 12 and 18

Find the Greatest Common Factor (GCF) of 12 and 18 with a complete step-by-step solution. The GCF is the largest number that divides both numbers without leaving a remainder.

Answer: GCF(12, 18) = 6

Step-by-Step Solution

Step 1 Find the Factors of 12

To find the GCF of 12 and 18, we first need to find all factors of each number.

The factors of 12 are numbers that divide 12 evenly:

1 × 12 = 12, 2 × 6 = 12, 3 × 4 = 12

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

Step 2 Find the Factors of 18

Now we find all factors of 18:

1 × 18 = 18, 2 × 9 = 18, 3 × 6 = 18

Factors of 18: 1, 2, 3, 6, 9, 18

Step 3 Find the Common Factors

The common factors are numbers that appear in both lists:

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

Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6

The Greatest Common Factor is the largest of these: 6

Step 4 Prime Factorization Method

We can also find the GCF using prime factorization:

12 = 2^2 × 3

18 = 2 × 3^2

Take the common prime factors with the lowest powers:

GCF = 2 × 3 = 6

Step 5 Euclidean Algorithm

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

18 = 1 × 12 + 6

12 = 2 × 6 + 0

When the remainder is 0, the GCF is the last divisor: 6

Step 6 Final Answer

GCF(12, 18) = 6

GCF of 12 and 18

Related Calculations