# Prime factorization of $2045$

The calculator will find the prime factorization of $2045$, with steps shown.

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Find the prime factorization of $2045$.

### Solution

Start with the number $2$.

Determine whether $2045$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2045$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2045$ is divisible by $5$.

It is divisible, thus, divide $2045$ by ${\color{green}5}$: $\frac{2045}{5} = {\color{red}409}$.

The prime number ${\color{green}409}$ has no other factors then $1$ and ${\color{green}409}$: $\frac{409}{409} = {\color{red}1}$.

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: $2045 = 5 \cdot 409$.

The prime factorization is $2045 = 5 \cdot 409$A.