Chapter SR4, Problem 29P

Solution

The greatest common factor (GCF) of the numbers $7,12,\text{and }17$ .

  $1$

Given:

The pair of numbers $7,12,\text{and }17$ .

Concept Used:

The GCF (Greatest Common Factor) of a list of integers is the largest integer that is a factor of all the integers in the list.

GCF (Greatest Common Factor) of a list of numbers can be found using following steps,

1. Write prime factorization of each number
2. Find the product of common factors that appear in each number.

Calculation:

In order to find the greatest common factor of the given numbers $7,12,\text{and }17$ , find the prime factorization of each number and then multiply the common factors that are common in each number to get the GCF of the numbers as shown below,

  $\begin{array}{l}\text{Prime factors of }7,12,\text{and }17\text{:}\\ 7=7\times 1\\ 12=2\times 2\times 3\times 1\\ 17=17\times 1\\ \\ \text{GCF of }7,12,\text{and }17\text{ is:}\\ 1\end{array}$

Thus, the greatest common factor (GCF) of the given numbers is $1$ .