# Prime factorization of $735$

The calculator will find the prime factorization of $735$, with steps shown.

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Find the prime factorization of $735$.

### Solution

Start with the number $2$.

Determine whether $735$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $735$ is divisible by $3$.

It is divisible, thus, divide $735$ by ${\color{green}3}$: $\frac{735}{3} = {\color{red}245}$.

Determine whether $245$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $245$ is divisible by $5$.

It is divisible, thus, divide $245$ by ${\color{green}5}$: $\frac{245}{5} = {\color{red}49}$.

Determine whether $49$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $49$ is divisible by $7$.

It is divisible, thus, divide $49$ by ${\color{green}7}$: $\frac{49}{7} = {\color{red}7}$.

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: $735 = 3 \cdot 5 \cdot 7^{2}$.

The prime factorization is $735 = 3 \cdot 5 \cdot 7^{2}$A.