# Prime factorization of $354$

The calculator will find the prime factorization of $354$, with steps shown.

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Find the prime factorization of $354$.

### Solution

Start with the number $2$.

Determine whether $354$ is divisible by $2$.

It is divisible, thus, divide $354$ by ${\color{green}2}$: $\frac{354}{2} = {\color{red}177}$.

Determine whether $177$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $177$ is divisible by $3$.

It is divisible, thus, divide $177$ by ${\color{green}3}$: $\frac{177}{3} = {\color{red}59}$.

The prime number ${\color{green}59}$ has no other factors then $1$ and ${\color{green}59}$: $\frac{59}{59} = {\color{red}1}$.

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: $354 = 2 \cdot 3 \cdot 59$.

The prime factorization is $354 = 2 \cdot 3 \cdot 59$A.