# Prime factorization of $1000$

The calculator will find the prime factorization of $1000$, with steps shown.

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Find the prime factorization of $1000$.

### Solution

Start with the number $2$.

Determine whether $1000$ is divisible by $2$.

It is divisible, thus, divide $1000$ by ${\color{green}2}$: $\frac{1000}{2} = {\color{red}500}$.

Determine whether $500$ is divisible by $2$.

It is divisible, thus, divide $500$ by ${\color{green}2}$: $\frac{500}{2} = {\color{red}250}$.

Determine whether $250$ is divisible by $2$.

It is divisible, thus, divide $250$ by ${\color{green}2}$: $\frac{250}{2} = {\color{red}125}$.

Determine whether $125$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $125$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $125$ is divisible by $5$.

It is divisible, thus, divide $125$ by ${\color{green}5}$: $\frac{125}{5} = {\color{red}25}$.

Determine whether $25$ is divisible by $5$.

It is divisible, thus, divide $25$ by ${\color{green}5}$: $\frac{25}{5} = {\color{red}5}$.

The prime number ${\color{green}5}$ has no other factors then $1$ and ${\color{green}5}$: $\frac{5}{5} = {\color{red}1}$.

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: $1000 = 2^{3} \cdot 5^{3}$.

The prime factorization is $1000 = 2^{3} \cdot 5^{3}$A.