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 both lists is $\,3\,.$ In other words, the only factor that is common to both lists is $\,3\,.$
Thought process: The factors of $\,3x\,$ are $\,3\,$ and $\,x\,.$ The factors of $\,\,3t\,\,$ are $\,3\,$ and $\,\,t\,.$ The only factor that appears in 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 $\,x-k\,$ inside parentheses.
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 first expression.
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.