# Prime factorization of $369$

The calculator will find the prime factorization of $369$, with steps shown.

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Find the prime factorization of $369$.

### Solution

Start with the number $2$.

Determine whether $369$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $369$ is divisible by $3$.

It is divisible, thus, divide $369$ by ${\color{green}3}$: $\frac{369}{3} = {\color{red}123}$.

Determine whether $123$ is divisible by $3$.

It is divisible, thus, divide $123$ by ${\color{green}3}$: $\frac{123}{3} = {\color{red}41}$.

The prime number ${\color{green}41}$ has no other factors then $1$ and ${\color{green}41}$: $\frac{41}{41} = {\color{red}1}$.

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: $369 = 3^{2} \cdot 41$.

The prime factorization is $369 = 3^{2} \cdot 41$A.