Chapter 1.1, Problem 19CCR

To determine

The greatest common factor (GCF) of $35\text{ and }14$ .

Answer to Problem 19CCR

  $7$

Explanation of Solution

Given:

The pair of numbers, $35\text{ and }14$

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 $35\text{ and }14$ , firstlist the prime factors of each number, as

  $\begin{array}{l}35=5\times 7\\ 14=2\times 7\end{array}$

Here observe that both the numbers have 7 as common factor in them. So, the greatest common factor (GCF) of the pair of numbers is 7.