# Identifying Common Factors

## Examples

Question: Identify all common factor(s) of $\,3x\,$ and $\,3t\,.$

Answer:
$3$

Thought process: The factors of $\,3x\,$ are $\,3\,$ and $\,x\,.$ The factors of $\,\,3t\,\,$ are $\,3\,$ and $\,\,t\,.$ The only factor that appears in

Thought process: The factors of $\,3x\,$ are $\,3\,$ and $\,x\,.$ The factors of $\,\,3t\,\,$ are $\,3\,$ and $\,\,t\,.$ The only factor that appears in

*both*lists is $\,3\,.$ In other words, the only factor that is*common*to both lists is $\,3\,.$
Question:
Identify all common factor(s) of
$\,xy\,$ and $\,zx\,.$

Answer:
$x$

Question:
Identify all common factor(s) of
$\,3(x+1)\,$ and
$\,(x+1)(x-2)\,.$

Answer:
$(x+1)$

Note: Input any common factor of the form $\,x+k\,$ or $\,x-k\,$

Note: Input any common factor of the form $\,x+k\,$ or $\,x-k\,$

*inside parentheses*.
Question:
Identify all common factor(s) of
$\,7txy\,$ and
$\,7zyx\,.$

Answer:
$7xy$

Note: List the common factor(s) in the order that they appear, going from left to right, in the

Note: List the common factor(s) in the order that they appear, going from left to right, in the

*first*expression.
Question:
Identify all common factor(s) of
$\,3x^2y^3\,$ and
$\,4y^3\,.$

Answer:
$y^3$

Note: Input exponents using the ‘ ^ ’ key.

Note: Input exponents using the ‘ ^ ’ key.