# Prime factorization of $3364$

The calculator will find the prime factorization of $3364$, with steps shown.

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Find the prime factorization of $3364$.

### Solution

Start with the number $2$.

Determine whether $3364$ is divisible by $2$.

It is divisible, thus, divide $3364$ by ${\color{green}2}$: $\frac{3364}{2} = {\color{red}1682}$.

Determine whether $1682$ is divisible by $2$.

It is divisible, thus, divide $1682$ by ${\color{green}2}$: $\frac{1682}{2} = {\color{red}841}$.

Determine whether $841$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $841$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $841$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $841$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $841$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $841$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $841$ is divisible by $17$.

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

The next prime number is $19$.

Determine whether $841$ is divisible by $19$.

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

The next prime number is $23$.

Determine whether $841$ is divisible by $23$.

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

The next prime number is $29$.

Determine whether $841$ is divisible by $29$.

It is divisible, thus, divide $841$ by ${\color{green}29}$: $\frac{841}{29} = {\color{red}29}$.

The prime number ${\color{green}29}$ has no other factors then $1$ and ${\color{green}29}$: $\frac{29}{29} = {\color{red}1}$.

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: $3364 = 2^{2} \cdot 29^{2}$.

The prime factorization is $3364 = 2^{2} \cdot 29^{2}$A.