Question
Using prime factorization method, find the following numbers are perfect squares$?$
$2916$
$2916$
✓
Answer
$2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3$
$\begin{array}{c|c} 2& 2916 \\ \hline 2 & 1458 \\\hline 3&729 \\\hline 3&243 \\\hline 3&81 \\\hline 3&27 \\\hline 3&9 \\\hline 3&3 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
$2916 = (2 × 2) × (3 × 3) × (3 × 3) × (3 × 3)$
There are no left out of pairs. Hence, $2916$ is a perfect square.
$\begin{array}{c|c} 2& 2916 \\ \hline 2 & 1458 \\\hline 3&729 \\\hline 3&243 \\\hline 3&81 \\\hline 3&27 \\\hline 3&9 \\\hline 3&3 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
$2916 = (2 × 2) × (3 × 3) × (3 × 3) × (3 × 3)$
There are no left out of pairs. Hence, $2916$ is a perfect square.
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