# Prime factorization of $3768$

The calculator will find the prime factorization of $3768$, with steps shown.

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Find the prime factorization of $3768$.

### Solution

Start with the number $2$.

Determine whether $3768$ is divisible by $2$.

It is divisible, thus, divide $3768$ by ${\color{green}2}$: $\frac{3768}{2} = {\color{red}1884}$.

Determine whether $1884$ is divisible by $2$.

It is divisible, thus, divide $1884$ by ${\color{green}2}$: $\frac{1884}{2} = {\color{red}942}$.

Determine whether $942$ is divisible by $2$.

It is divisible, thus, divide $942$ by ${\color{green}2}$: $\frac{942}{2} = {\color{red}471}$.

Determine whether $471$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $471$ is divisible by $3$.

It is divisible, thus, divide $471$ by ${\color{green}3}$: $\frac{471}{3} = {\color{red}157}$.

The prime number ${\color{green}157}$ has no other factors then $1$ and ${\color{green}157}$: $\frac{157}{157} = {\color{red}1}$.

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: $3768 = 2^{3} \cdot 3 \cdot 157$.

The prime factorization is $3768 = 2^{3} \cdot 3 \cdot 157$A.