# Prime factorization of $4396$

The calculator will find the prime factorization of $4396$, with steps shown.

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Find the prime factorization of $4396$.

### Solution

Start with the number $2$.

Determine whether $4396$ is divisible by $2$.

It is divisible, thus, divide $4396$ by ${\color{green}2}$: $\frac{4396}{2} = {\color{red}2198}$.

Determine whether $2198$ is divisible by $2$.

It is divisible, thus, divide $2198$ by ${\color{green}2}$: $\frac{2198}{2} = {\color{red}1099}$.

Determine whether $1099$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1099$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1099$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1099$ is divisible by $7$.

It is divisible, thus, divide $1099$ by ${\color{green}7}$: $\frac{1099}{7} = {\color{red}157}$.

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: $4396 = 2^{2} \cdot 7 \cdot 157$.

The prime factorization is $4396 = 2^{2} \cdot 7 \cdot 157$A.