# Prime factorization of $3456$

The calculator will find the prime factorization of $3456$, with steps shown.

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Find the prime factorization of $3456$.

### Solution

Start with the number $2$.

Determine whether $3456$ is divisible by $2$.

It is divisible, thus, divide $3456$ by ${\color{green}2}$: $\frac{3456}{2} = {\color{red}1728}$.

Determine whether $1728$ is divisible by $2$.

It is divisible, thus, divide $1728$ by ${\color{green}2}$: $\frac{1728}{2} = {\color{red}864}$.

Determine whether $864$ is divisible by $2$.

It is divisible, thus, divide $864$ by ${\color{green}2}$: $\frac{864}{2} = {\color{red}432}$.

Determine whether $432$ is divisible by $2$.

It is divisible, thus, divide $432$ by ${\color{green}2}$: $\frac{432}{2} = {\color{red}216}$.

Determine whether $216$ is divisible by $2$.

It is divisible, thus, divide $216$ by ${\color{green}2}$: $\frac{216}{2} = {\color{red}108}$.

Determine whether $108$ is divisible by $2$.

It is divisible, thus, divide $108$ by ${\color{green}2}$: $\frac{108}{2} = {\color{red}54}$.

Determine whether $54$ is divisible by $2$.

It is divisible, thus, divide $54$ by ${\color{green}2}$: $\frac{54}{2} = {\color{red}27}$.

Determine whether $27$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $27$ is divisible by $3$.

It is divisible, thus, divide $27$ by ${\color{green}3}$: $\frac{27}{3} = {\color{red}9}$.

Determine whether $9$ is divisible by $3$.

It is divisible, thus, divide $9$ by ${\color{green}3}$: $\frac{9}{3} = {\color{red}3}$.

The prime number ${\color{green}3}$ has no other factors then $1$ and ${\color{green}3}$: $\frac{3}{3} = {\color{red}1}$.

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: $3456 = 2^{7} \cdot 3^{3}$.

The prime factorization is $3456 = 2^{7} \cdot 3^{3}$A.