# Prime factorization of $3840$

The calculator will find the prime factorization of $3840$, with steps shown.

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Find the prime factorization of $3840$.

### Solution

Start with the number $2$.

Determine whether $3840$ is divisible by $2$.

It is divisible, thus, divide $3840$ by ${\color{green}2}$: $\frac{3840}{2} = {\color{red}1920}$.

Determine whether $1920$ is divisible by $2$.

It is divisible, thus, divide $1920$ by ${\color{green}2}$: $\frac{1920}{2} = {\color{red}960}$.

Determine whether $960$ is divisible by $2$.

It is divisible, thus, divide $960$ by ${\color{green}2}$: $\frac{960}{2} = {\color{red}480}$.

Determine whether $480$ is divisible by $2$.

It is divisible, thus, divide $480$ by ${\color{green}2}$: $\frac{480}{2} = {\color{red}240}$.

Determine whether $240$ is divisible by $2$.

It is divisible, thus, divide $240$ by ${\color{green}2}$: $\frac{240}{2} = {\color{red}120}$.

Determine whether $120$ is divisible by $2$.

It is divisible, thus, divide $120$ by ${\color{green}2}$: $\frac{120}{2} = {\color{red}60}$.

Determine whether $60$ is divisible by $2$.

It is divisible, thus, divide $60$ by ${\color{green}2}$: $\frac{60}{2} = {\color{red}30}$.

Determine whether $30$ is divisible by $2$.

It is divisible, thus, divide $30$ by ${\color{green}2}$: $\frac{30}{2} = {\color{red}15}$.

Determine whether $15$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $15$ is divisible by $3$.

It is divisible, thus, divide $15$ by ${\color{green}3}$: $\frac{15}{3} = {\color{red}5}$.

The prime number ${\color{green}5}$ has no other factors then $1$ and ${\color{green}5}$: $\frac{5}{5} = {\color{red}1}$.

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: $3840 = 2^{8} \cdot 3 \cdot 5$.

The prime factorization is $3840 = 2^{8} \cdot 3 \cdot 5$A.