# Prime factorization of $1364$

The calculator will find the prime factorization of $1364$, with steps shown.

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Find the prime factorization of $1364$.

### Solution

Start with the number $2$.

Determine whether $1364$ is divisible by $2$.

It is divisible, thus, divide $1364$ by ${\color{green}2}$: $\frac{1364}{2} = {\color{red}682}$.

Determine whether $682$ is divisible by $2$.

It is divisible, thus, divide $682$ by ${\color{green}2}$: $\frac{682}{2} = {\color{red}341}$.

Determine whether $341$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $341$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $341$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $341$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $341$ is divisible by $11$.

It is divisible, thus, divide $341$ by ${\color{green}11}$: $\frac{341}{11} = {\color{red}31}$.

The prime number ${\color{green}31}$ has no other factors then $1$ and ${\color{green}31}$: $\frac{31}{31} = {\color{red}1}$.

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: $1364 = 2^{2} \cdot 11 \cdot 31$.

The prime factorization is $1364 = 2^{2} \cdot 11 \cdot 31$A.