# Prime factorization of $3465$

The calculator will find the prime factorization of $3465$, with steps shown.

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Find the prime factorization of $3465$.

### Solution

Start with the number $2$.

Determine whether $3465$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3465$ is divisible by $3$.

It is divisible, thus, divide $3465$ by ${\color{green}3}$: $\frac{3465}{3} = {\color{red}1155}$.

Determine whether $1155$ is divisible by $3$.

It is divisible, thus, divide $1155$ by ${\color{green}3}$: $\frac{1155}{3} = {\color{red}385}$.

Determine whether $385$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $385$ is divisible by $5$.

It is divisible, thus, divide $385$ by ${\color{green}5}$: $\frac{385}{5} = {\color{red}77}$.

Determine whether $77$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $77$ is divisible by $7$.

It is divisible, thus, divide $77$ by ${\color{green}7}$: $\frac{77}{7} = {\color{red}11}$.

The prime number ${\color{green}11}$ has no other factors then $1$ and ${\color{green}11}$: $\frac{11}{11} = {\color{red}1}$.

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: $3465 = 3^{2} \cdot 5 \cdot 7 \cdot 11$.

The prime factorization is $3465 = 3^{2} \cdot 5 \cdot 7 \cdot 11$A.