# Prime factorization of $4041$

The calculator will find the prime factorization of $4041$, with steps shown.

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Find the prime factorization of $4041$.

### Solution

Start with the number $2$.

Determine whether $4041$ is divisible by $2$.

Since it is not divisible, move to the next prime number.

The next prime number is $3$.

Determine whether $4041$ is divisible by $3$.

It is divisible, thus, divide $4041$ by ${\color{green}3}$: $\frac{4041}{3} = {\color{red}1347}$.

Determine whether $1347$ is divisible by $3$.

It is divisible, thus, divide $1347$ by ${\color{green}3}$: $\frac{1347}{3} = {\color{red}449}$.

The prime number ${\color{green}449}$ has no other factors then $1$ and ${\color{green}449}$: $\frac{449}{449} = {\color{red}1}$.

Since we have obtained $1$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $4041 = 3^{2} \cdot 449$.

The prime factorization is $4041 = 3^{2} \cdot 449$A.