Find the greatest common factor of the given expression. $15 z ^ { 4 } c ^ { 6 } , 10 z ^ { 3 } c ^ { 7 } \text { and } 55 z ^ { 6 } c ^ { 2 }$
A) $2 c ^ { 5 }$
B) $5 z c ^ { 4 }$
C) $3 z ^ { 8 } c ^ { 2 }$
D) $5 z ^ { 3 } c ^ { 2 }$

Question

Quizplus · Accepted Answer

We can use the method of prime factorization to find the GCF of the given expressions. First, we can write each expression as a product of its prime factors:

$15 z^4 c^6 = 3 \cdot 5 \cdot z \cdot z \cdot z \cdot z \cdot c \cdot c \cdot c \cdot c \cdot c \cdot c$
$10 z^3 c^7 = 2 \cdot 5 \cdot z \cdot z \cdot z \cdot c \cdot c \cdot c \cdot c \cdot c \cdot c \cdot c$
$55 z^6 c^2 = 5 \cdot 11 \cdot z \cdot z \cdot z \cdot z \cdot z \cdot z \cdot c \cdot c$

To find the GCF of these expressions, we can look for the prime factors that are present in all three expressions. These include $5$, $z^3$, and $c^2$. Therefore, the GCF is $5z^3c^2$. The best choice that matches this result is D.

Find the Greatest Common Factor of the Given Expression 15z4c6,10z3c7 and 55z6c215 z ^ { 4 } c ^ { 6 } , 10 z ^ { 3 } c ^ { 7 } \text { and } 55 z ^ { 6 } c ^ { 2 }15z4c6,10z3c7 and 55z6c2

Find the Greatest Common Factor of the Given Expression $15 z ^ { 4 } c ^ { 6 } , 10 z ^ { 3 } c ^ { 7 } \text { and } 55 z ^ { 6 } c ^ { 2 }$