Find the greatest common factor of the given expressions. $45 z d , 40 z d ^ { 5 } \text { and } 65 z ^ { 2 } d$
A) $9 \mathrm { zd }$
B) $5 z d$
C) $8 d z$
D) $5 z d ^ { 2 }$

Question

Quizplus · Accepted Answer

To find the greatest common factor, we need to find the factors that are common to all three expressions. 
Breaking each expression down into its prime factors: 
$45zd = 3^2 \cdot 5 \cdot z \cdot d$
$40zd^5 = 2^3 \cdot 5 \cdot z \cdot d^5$
$65z^2d = 5 \cdot 13 \cdot z^2 \cdot d$
The factors that are common to all three expressions are $5$, $z$, and $d$. The highest power of $5$ that occurs in any expression is $5^1$, the highest power of $z$ that occurs in any expression is $z^1$, and the highest power of $d$ that occurs in any expression is $d^1$. Therefore, the greatest common factor is $5zd$.

Find the Greatest Common Factor of the Given Expressions 45zd,40zd5 and 65z2d45 z d , 40 z d ^ { 5 } \text { and } 65 z ^ { 2 } d45zd,40zd5 and 65z2d

Find the Greatest Common Factor of the Given Expressions $45 z d , 40 z d ^ { 5 } \text { and } 65 z ^ { 2 } d$