Chapter 4.5, Problem 72E

To determine

To find the greatest common factor of $42x^{3}y,70x{y}^2$ .

Answer to Problem 72E

  $14xy$

Explanation of Solution

Given information: $42x^{3}y,70x{y}^2$

Calculation: 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.

Given, $42x^{3}y,70x{y}^2$

First, find the greatest common factors of 42 and 70.

Factors of $42=1,2,3,6,7,14,21,42$

Factors of $70=1,2,5,7,10,14,35,70$

Highest common factor of 42 and 70 $=14$

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

Factors of $x^{3}y=x\times x\times x\times y$

Factors of $x{y}^2=x\times y\times y$

Greatest common factor of $x^{3}y\&x{y}^2=x\times y$

Hence, the greatest common factor of the two algebraic expressions

  $=14\times xy$

  $=14xy$ This is the greatest common factor.