Chapter 8.4, Problem 45E

To determine

To find:

The greatest common factor of the given numbers.

Answer to Problem 45E

The greatest common factor of 15 and 48is 3.

Explanation of Solution

Given:

Twonumbers: $15,\text{48}$ .

Concept used:

To find Greatest common factors of two or more numbers, we find prime factors of each number and then multiply the common factors of each number.

When two or more numbers have no common factors, then 1 is the greatest common factor of the numbers.

Calculation:

First of all, we will find the prime factors of our given numbers as:

  $\begin{array}{l}\text{Prime factors of 15:}3\times 5\\ \text{Prime factors of 48:}2\times 2\times 2\times 2\times 3\end{array}$

Upon looking at prime factors of 15 and 48, we can see that the common factor of both numbers is $3$ .

Therefore, the greatest common factor of 15 and 48would be $3$ .