# Prime factorization of $3008$

The calculator will find the prime factorization of $3008$, with steps shown.

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Find the prime factorization of $3008$.

### Solution

Start with the number $2$.

Determine whether $3008$ is divisible by $2$.

It is divisible, thus, divide $3008$ by ${\color{green}2}$: $\frac{3008}{2} = {\color{red}1504}$.

Determine whether $1504$ is divisible by $2$.

It is divisible, thus, divide $1504$ by ${\color{green}2}$: $\frac{1504}{2} = {\color{red}752}$.

Determine whether $752$ is divisible by $2$.

It is divisible, thus, divide $752$ by ${\color{green}2}$: $\frac{752}{2} = {\color{red}376}$.

Determine whether $376$ is divisible by $2$.

It is divisible, thus, divide $376$ by ${\color{green}2}$: $\frac{376}{2} = {\color{red}188}$.

Determine whether $188$ is divisible by $2$.

It is divisible, thus, divide $188$ by ${\color{green}2}$: $\frac{188}{2} = {\color{red}94}$.

Determine whether $94$ is divisible by $2$.

It is divisible, thus, divide $94$ by ${\color{green}2}$: $\frac{94}{2} = {\color{red}47}$.

The prime number ${\color{green}47}$ has no other factors then $1$ and ${\color{green}47}$: $\frac{47}{47} = {\color{red}1}$.

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: $3008 = 2^{6} \cdot 47$.

The prime factorization is $3008 = 2^{6} \cdot 47$A.