# Prime factorization of $1755$

The calculator will find the prime factorization of $1755$, with steps shown.

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Find the prime factorization of $1755$.

### Solution

Start with the number $2$.

Determine whether $1755$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1755$ is divisible by $3$.

It is divisible, thus, divide $1755$ by ${\color{green}3}$: $\frac{1755}{3} = {\color{red}585}$.

Determine whether $585$ is divisible by $3$.

It is divisible, thus, divide $585$ by ${\color{green}3}$: $\frac{585}{3} = {\color{red}195}$.

Determine whether $195$ is divisible by $3$.

It is divisible, thus, divide $195$ by ${\color{green}3}$: $\frac{195}{3} = {\color{red}65}$.

Determine whether $65$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $65$ is divisible by $5$.

It is divisible, thus, divide $65$ by ${\color{green}5}$: $\frac{65}{5} = {\color{red}13}$.

The prime number ${\color{green}13}$ has no other factors then $1$ and ${\color{green}13}$: $\frac{13}{13} = {\color{red}1}$.

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: $1755 = 3^{3} \cdot 5 \cdot 13$.

The prime factorization is $1755 = 3^{3} \cdot 5 \cdot 13$A.