# Prime factorization of $4560$

The calculator will find the prime factorization of $4560$, with steps shown.

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Find the prime factorization of $4560$.

### Solution

Start with the number $2$.

Determine whether $4560$ is divisible by $2$.

It is divisible, thus, divide $4560$ by ${\color{green}2}$: $\frac{4560}{2} = {\color{red}2280}$.

Determine whether $2280$ is divisible by $2$.

It is divisible, thus, divide $2280$ by ${\color{green}2}$: $\frac{2280}{2} = {\color{red}1140}$.

Determine whether $1140$ is divisible by $2$.

It is divisible, thus, divide $1140$ by ${\color{green}2}$: $\frac{1140}{2} = {\color{red}570}$.

Determine whether $570$ is divisible by $2$.

It is divisible, thus, divide $570$ by ${\color{green}2}$: $\frac{570}{2} = {\color{red}285}$.

Determine whether $285$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $285$ is divisible by $3$.

It is divisible, thus, divide $285$ by ${\color{green}3}$: $\frac{285}{3} = {\color{red}95}$.

Determine whether $95$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $95$ is divisible by $5$.

It is divisible, thus, divide $95$ by ${\color{green}5}$: $\frac{95}{5} = {\color{red}19}$.

The prime number ${\color{green}19}$ has no other factors then $1$ and ${\color{green}19}$: $\frac{19}{19} = {\color{red}1}$.

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: $4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19$.

The prime factorization is $4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19$A.