# Prime factorization of $4401$

The calculator will find the prime factorization of $4401$, with steps shown.

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Find the prime factorization of $4401$.

### Solution

Start with the number $2$.

Determine whether $4401$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4401$ is divisible by $3$.

It is divisible, thus, divide $4401$ by ${\color{green}3}$: $\frac{4401}{3} = {\color{red}1467}$.

Determine whether $1467$ is divisible by $3$.

It is divisible, thus, divide $1467$ by ${\color{green}3}$: $\frac{1467}{3} = {\color{red}489}$.

Determine whether $489$ is divisible by $3$.

It is divisible, thus, divide $489$ by ${\color{green}3}$: $\frac{489}{3} = {\color{red}163}$.

The prime number ${\color{green}163}$ has no other factors then $1$ and ${\color{green}163}$: $\frac{163}{163} = {\color{red}1}$.

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: $4401 = 3^{3} \cdot 163$.

The prime factorization is $4401 = 3^{3} \cdot 163$A.