# Prime factorization of $1065$

The calculator will find the prime factorization of $1065$, with steps shown.

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Find the prime factorization of $1065$.

### Solution

Start with the number $2$.

Determine whether $1065$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1065$ is divisible by $3$.

It is divisible, thus, divide $1065$ by ${\color{green}3}$: $\frac{1065}{3} = {\color{red}355}$.

Determine whether $355$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $355$ is divisible by $5$.

It is divisible, thus, divide $355$ by ${\color{green}5}$: $\frac{355}{5} = {\color{red}71}$.

The prime number ${\color{green}71}$ has no other factors then $1$ and ${\color{green}71}$: $\frac{71}{71} = {\color{red}1}$.

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: $1065 = 3 \cdot 5 \cdot 71$.

The prime factorization is $1065 = 3 \cdot 5 \cdot 71$A.