Chapter 4.5, Problem 73E

To determine

To find the greatest common factor of $100x^3,75y^3$ .

Answer to Problem 73E

25

Explanation of Solution

Given information: $100x^3,75y^3$

To find the greatest common factor of two or more algebraic expressions, find the greatest common factors of the numbers and the variables separately. After finding the two, multiply them, to reach the greatest common factors of the expressions combined.

Calculation:

Given, $100x^3,75y^3$

First, find the greatest common factors of 100 and 75.

Factors of $100=1,2,4,5,10,20,25,50,100$

Factors of $75=1,3,5,15,25,75$

Highest common factor of 100 and 75 $=25$

Second, find the greatest common factor of $x^{3}y\&x{y}^2$

Factors of $x^3=x\times x\times x$

Factors of $y^3=y\times y\times y$

Greatest common factor of $x^3\&y^3=1$ Here, since there are no common terms in $x^3\&y^3$ , the greatest common factor is 1.

Hence, the greatest common factor of the two algebraic expressions

  $=25\times 1$

  $=25$ This is the greatest common factor.