# Prime factorization of $1465$

The calculator will find the prime factorization of $1465$, with steps shown.

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Find the prime factorization of $1465$.

### Solution

Start with the number $2$.

Determine whether $1465$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1465$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1465$ is divisible by $5$.

It is divisible, thus, divide $1465$ by ${\color{green}5}$: $\frac{1465}{5} = {\color{red}293}$.

The prime number ${\color{green}293}$ has no other factors then $1$ and ${\color{green}293}$: $\frac{293}{293} = {\color{red}1}$.

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: $1465 = 5 \cdot 293$.

The prime factorization is $1465 = 5 \cdot 293$A.