What is the GCF of 18 and 60?

GCF of 18 and 60

Answer: The greatest common factor (GCF) of 18 and 60 is 6.

Solution: To find the greatest common factor (GCF) of 18 and 60, we can use the prime factorization method:

Step 1: Find the prime factorization of each number.

For 18:

$$18 = 2 \times 9$$ 

$$18 = 2 \times 3 \times 3$$ 

So, the prime factorization of 18 is \(2^1 \times 3^2\).

For 60:

$$60 = 2 \times 30$$ 

$$60 = 2 \times 2 \times 15$$ 

$$60 = 2 \times 2 \times 3 \times 5$$ 

So, the prime factorization of 60 is \(2^2 \times 3^1 \times 5^1\).

Step 2: Identify the common prime factors and their lowest powers.

The common prime factors are 2 and 3.

For the prime factor 2:

In the factorization of 18, 2 appears as \(2^1\).

In the factorization of 60, 2 appears as \(2^2\).

The lowest power of 2 is \(2^1\).

For the prime factor 3:

In the factorization of 18, 3 appears as \(3^2\).

In the factorization of 60, 3 appears as \(3^1\).

The lowest power of 3 is \(3^1\).

Step 3: Multiply the common prime factors raised to their lowest powers.

$$GCF(18, 60) = 2^1 \times 3^1$$ 

$$GCF(18, 60) = 2 \times 3$$ 

$$GCF(18, 60) = 6$$

Thus, the greatest common factor of 18 and 60 is 6.