Question

find the greatest common factor of the expressions
$14c^3x$
$4cx^2$
$6c^2x^5$
show your work here
hint: to add an exponent ($a^b$), type \exponent\ or press \^\
enter your answer

find the greatest common factor of the expressions
$9w^6k$
$33w^3k^2$
$21w^3k^3$
show your work here
hint: to add an exponent ($a^b$), type \exponent\ or press \^\

Explanation:

Step1: GCF of coefficients 14,4,6

Prime factors: $14=2\times7$, $4=2^2$, $6=2\times3$. GCF is $2$.

Step2: GCF of $c$-terms: $c^3,c,c^2$

Choose lowest exponent: $c^1=c$.

Step3: GCF of $x$-terms: $x,x^2,x^5$

Choose lowest exponent: $x^1=x$.

Step4: Combine for first set

Multiply GCFs: $2\times c\times x = 2cx$.

Step5: GCF of coefficients 9,33,21

Prime factors: $9=3^2$, $33=3\times11$, $21=3\times7$. GCF is $3$.

Step6: GCF of $w$-terms: $w^6,w^3,w^3$

Choose lowest exponent: $w^3$.

Step7: GCF of $k$-terms: $k,k^2,k^3$

Choose lowest exponent: $k^1=k$.

Step8: Combine for second set

Multiply GCFs: $3\times w^3\times k = 3w^3k$.

Answer:

1. $2cx$
2. $3w^3k$