Question

find the gcf (greatest common factor) of the following terms.

\\{14, 10, 45\\}

Explanation:

Find the prime factorization of each number

To find the greatest common factor, we first write each number as a product of its prime factors.
Using the Greatest Common Factor knowledge point:

$$
LATEXBLOCK0
$$

Identify the common prime factors

Next, we look for any prime factors that are shared by all three numbers:

• The prime factors of \(14\) are \(2\) and \(7\).
• The prime factors of \(10\) are \(2\) and \(5\).
• The prime factors of \(45\) are \(3\) and \(5\).

There is no prime number that appears in the factorization of all three numbers.

Determine the greatest common factor

Since there are no common prime factors shared among \(14\), \(10\), and \(45\), the only common factor they all share is \(1\).
Therefore, the greatest common factor (GCF) is \(1\).

Answer:

1