Question
Find the square root of the following by prime factorization.3013696
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Answer
Resolving 3013696 into prime factors,
3013696 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 31 × 31
$\begin{array}{c|c}2&3013696 \\ \hline 2 & 1506848 \\\hline 2&753424\\\hline2&376712 \\\hline2&188356\\\hline2&941781\\\hline7&47089\\\hline7&6727\\\hline31&961\\\hline31&31\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
3013696 = (2 × 2) × (2 × 2) × (2 × 2) × (7 × 7) × (31 × 31)
Taking one factor for each pair, we get the square root of 3013696
2 × 2 × 2 × 7 × 31 = 1736
3013696 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 31 × 31
$\begin{array}{c|c}2&3013696 \\ \hline 2 & 1506848 \\\hline 2&753424\\\hline2&376712 \\\hline2&188356\\\hline2&941781\\\hline7&47089\\\hline7&6727\\\hline31&961\\\hline31&31\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
3013696 = (2 × 2) × (2 × 2) × (2 × 2) × (7 × 7) × (31 × 31)
Taking one factor for each pair, we get the square root of 3013696
2 × 2 × 2 × 7 × 31 = 1736
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