# Prime factorization of $3605$

The calculator will find the prime factorization of $3605$, with steps shown.

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Find the prime factorization of $3605$.

### Solution

Start with the number $2$.

Determine whether $3605$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3605$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $3605$ is divisible by $5$.

It is divisible, thus, divide $3605$ by ${\color{green}5}$: $\frac{3605}{5} = {\color{red}721}$.

Determine whether $721$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $721$ is divisible by $7$.

It is divisible, thus, divide $721$ by ${\color{green}7}$: $\frac{721}{7} = {\color{red}103}$.

The prime number ${\color{green}103}$ has no other factors then $1$ and ${\color{green}103}$: $\frac{103}{103} = {\color{red}1}$.

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: $3605 = 5 \cdot 7 \cdot 103$.

The prime factorization is $3605 = 5 \cdot 7 \cdot 103$A.