Prime factorization of $$$1065$$$

Find the prime factorization of $$$1065$$$.

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.