# Prime factorization of $3225$

The calculator will find the prime factorization of $3225$, with steps shown.

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Find the prime factorization of $3225$.

### Solution

Start with the number $2$.

Determine whether $3225$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3225$ is divisible by $3$.

It is divisible, thus, divide $3225$ by ${\color{green}3}$: $\frac{3225}{3} = {\color{red}1075}$.

Determine whether $1075$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1075$ is divisible by $5$.

It is divisible, thus, divide $1075$ by ${\color{green}5}$: $\frac{1075}{5} = {\color{red}215}$.

Determine whether $215$ is divisible by $5$.

It is divisible, thus, divide $215$ by ${\color{green}5}$: $\frac{215}{5} = {\color{red}43}$.

The prime number ${\color{green}43}$ has no other factors then $1$ and ${\color{green}43}$: $\frac{43}{43} = {\color{red}1}$.

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: $3225 = 3 \cdot 5^{2} \cdot 43$.

The prime factorization is $3225 = 3 \cdot 5^{2} \cdot 43$A.