Question

What is the prime factorization of $3780$?

Answer 1

Determine the prime factorization of $3780$.

Prime numbers are whole numbers greater than one that can only be divided equally by themselves and one.

Divide $3780$ by only prime numbers to obtain the prime factorization.

The number $3780$ is divided by $2$, which is a prime number.

$\begin{array}{rcl}3780÷2& =& 1890\\ & \Rightarrow & 1890÷2=945\end{array}$

Now, $945$ is divided by $3$, which is a prime number.

$$\begin{gathered} \begin{array}{rcl}945÷3& =& 315\\ & \Rightarrow & 315÷3=105\end{array} \\ \begin{array}{rcl}& \Rightarrow & 105÷3=35\end{array} \end{gathered}$$

Now, $35$ is divided by $5$, which is a prime number.

$\begin{array}{rcl}35÷5& =& 7\end{array}$

Now, $7$ is divided by $7$, which is a prime number.

$\begin{array}{rcl}7÷7& =& 1\end{array}$

Thus, the prime factorization of $3780$ is obtained as follows:

$\begin{array}{rcl}3780& =& 2\times 2\times 3\times 3\times 3\times 5\times 7\\ & \Rightarrow & 3780=2^2\times 3^3\times 5\times 7\end{array}$

Hence, the prime factorization of $3780$ is $\begin{array}{rcl}& & 2^2\times 3^3\times 5\times 7\end{array}$.