Questions: Find the GCF for the following list. 18,30,60 The GCF is (Simplify your answer.)

Solution Steps

To find the Greatest Common Factor (GCF) of a list of numbers, we can use the Euclidean algorithm iteratively. First, find the GCF of the first two numbers, then use that result to find the GCF with the next number, and so on.

We are given the numbers \( 18, 30, \) and \( 60 \).

To find the GCF, we can use the Euclidean algorithm. We start by finding the GCF of the first two numbers:

1. \( \text{GCF}(18, 30) \):

   • The factors of \( 18 \) are \( 1, 2, 3, 6, 9, 18 \).
   • The factors of \( 30 \) are \( 1, 2, 3, 5, 6, 10, 15, 30 \).
   • The common factors are \( 1, 2, 3, 6 \), so \( \text{GCF}(18, 30) = 6 \).

2. Now, we find the GCF of the result with the next number:

   • \( \text{GCF}(6, 60) \):
   • The factors of \( 60 \) are \( 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 \).
   • The common factors are \( 1, 2, 3, 6 \), so \( \text{GCF}(6, 60) = 6 \).

Thus, the GCF of \( 18, 30, \) and \( 60 \) is \( 6 \).

Final Answer