# Prime factorization of $3650$

The calculator will find the prime factorization of $3650$, with steps shown.

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Find the prime factorization of $3650$.

### Solution

Start with the number $2$.

Determine whether $3650$ is divisible by $2$.

It is divisible, thus, divide $3650$ by ${\color{green}2}$: $\frac{3650}{2} = {\color{red}1825}$.

Determine whether $1825$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1825$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1825$ is divisible by $5$.

It is divisible, thus, divide $1825$ by ${\color{green}5}$: $\frac{1825}{5} = {\color{red}365}$.

Determine whether $365$ is divisible by $5$.

It is divisible, thus, divide $365$ by ${\color{green}5}$: $\frac{365}{5} = {\color{red}73}$.

The prime number ${\color{green}73}$ has no other factors then $1$ and ${\color{green}73}$: $\frac{73}{73} = {\color{red}1}$.

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: $3650 = 2 \cdot 5^{2} \cdot 73$.

The prime factorization is $3650 = 2 \cdot 5^{2} \cdot 73$A.