Chapter SR4, Problem 25P

Solution

The greatest common factor (GCF) of the numbers $70\text{and }90$ .

  $10$

Given:

The pair of numbers $70\text{and }90$ .

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 $70\text{and }90$ , 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,

  $\begin{array}{l}\text{Prime factors of }70\text{and }90\text{:}\\ 70=2\times 5\times 7\\ 90=2\times 3\times 3\times 5\\ \\ \text{GCF of }70\text{and }90\text{ is:}\\ 2\times 5=10\end{array}$

Thus, the greatest common factor (GCF) of the given numbers is $10$ .