Chapter 1.1, Problem 20CCR

To determine

The greatest common factor (GCF) of $36\text{ and 54}$ .

Answer to Problem 20CCR

  $18$

Explanation of Solution

Given:

The pair of numbers, $36\text{ and 54}$

Concept Used:

The greatest common factor, or GCF, of a list of numbers is the greatest factor that divides those numbers.

Calculation:

In order to find the GCF of a list of numbers, firstlist the prime factors of each number. And then identify the common factors from each number. The product of common factors will give the greatest common factor of the numbers. If there are no common prime factors, then the GCF is 1.

Here to find the greatest common factor of $36\text{ and 54}$ , firstlist the prime factors of each number, as

  $\begin{array}{l}36=2\times 2\times 3\times 3\\ 54=2\times 3\times 3\times 3\end{array}$

Here, observe that the numbers have 2, 3 and 3 as common factors in both. So, the greatest common factor (GCF) of the pair of numbers is,

  $2\times 3\times 3=18$

Thus, the greatest common factor (GCF) of the pair of numbers is 18.