Solution 1bc38cb4-a127-4731-b477-abe17b1e6012
Points: 1 pt
We can use a factor tree:
\begin{tikzpicture}[
level distance=11mm,
level 1/.style={sibling distance=54mm},
level 2/.style={sibling distance=27mm},
level 3/.style={sibling distance=14mm},
every node/.style={font=\normalsize},
edge from parent/.style={draw=bodytext, line width=0.7pt}
]
\node {$756$}
child { node {$28$}
child { node {$4$}
child { node {$2$} }
child { node {$2$} }
}
child { node {$7$} }
}
child { node {$27$}
child { node {$3$} }
child { node {$9$}
child { node {$3$} }
child { node {$3$} }
}
};
\end{tikzpicture}
The leaves are all prime, so
\[
756=(2)(2)(3)(3)(3)(7)=2^2\cdot 3^3\cdot 7.
\]
Final answer:
756=2^2\cdot 3^3\cdot 7