# Prime factorization of $1720$

The calculator will find the prime factorization of $1720$, with steps shown.

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Find the prime factorization of $1720$.

### Solution

Start with the number $2$.

Determine whether $1720$ is divisible by $2$.

It is divisible, thus, divide $1720$ by ${\color{green}2}$: $\frac{1720}{2} = {\color{red}860}$.

Determine whether $860$ is divisible by $2$.

It is divisible, thus, divide $860$ by ${\color{green}2}$: $\frac{860}{2} = {\color{red}430}$.

Determine whether $430$ is divisible by $2$.

It is divisible, thus, divide $430$ by ${\color{green}2}$: $\frac{430}{2} = {\color{red}215}$.

Determine whether $215$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $215$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $215$ is divisible by $5$.

It is divisible, thus, divide $215$ by ${\color{green}5}$: $\frac{215}{5} = {\color{red}43}$.

The prime number ${\color{green}43}$ has no other factors then $1$ and ${\color{green}43}$: $\frac{43}{43} = {\color{red}1}$.

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: $1720 = 2^{3} \cdot 5 \cdot 43$.

The prime factorization is $1720 = 2^{3} \cdot 5 \cdot 43$A.