Chapter 8.4, Problem 46E

To determine

To find:

The greatest common factor of the given numbers.

Answer to Problem 46E

The greatest common factor of 64 and 56is $8$ .

Explanation of Solution

Given:

Twonumbers: $64,\text{56}$ .

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:

  $\begin{array}{l}\text{Prime factors of 64:}2\times 2\times 2\times 2\times 2\times 2\\ \text{Prime factors of 56:}2\times 2\times 2\times 7\end{array}$

Upon looking at prime factors of 64 and 56, we can see that the common factors of both numbers are $2\times 2\times 2=8$ .

Therefore, the greatest common factor of 64 and 56would be $8$ .