# Prime factorization of $2835$

The calculator will find the prime factorization of $2835$, with steps shown.

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Find the prime factorization of $2835$.

### Solution

Start with the number $2$.

Determine whether $2835$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2835$ is divisible by $3$.

It is divisible, thus, divide $2835$ by ${\color{green}3}$: $\frac{2835}{3} = {\color{red}945}$.

Determine whether $945$ is divisible by $3$.

It is divisible, thus, divide $945$ by ${\color{green}3}$: $\frac{945}{3} = {\color{red}315}$.

Determine whether $315$ is divisible by $3$.

It is divisible, thus, divide $315$ by ${\color{green}3}$: $\frac{315}{3} = {\color{red}105}$.

Determine whether $105$ is divisible by $3$.

It is divisible, thus, divide $105$ by ${\color{green}3}$: $\frac{105}{3} = {\color{red}35}$.

Determine whether $35$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $35$ is divisible by $5$.

It is divisible, thus, divide $35$ by ${\color{green}5}$: $\frac{35}{5} = {\color{red}7}$.

The prime number ${\color{green}7}$ has no other factors then $1$ and ${\color{green}7}$: $\frac{7}{7} = {\color{red}1}$.

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: $2835 = 3^{4} \cdot 5 \cdot 7$.

The prime factorization is $2835 = 3^{4} \cdot 5 \cdot 7$A.