# Prime factorization of $4380$

The calculator will find the prime factorization of $4380$, with steps shown.

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Find the prime factorization of $4380$.

### Solution

Start with the number $2$.

Determine whether $4380$ is divisible by $2$.

It is divisible, thus, divide $4380$ by ${\color{green}2}$: $\frac{4380}{2} = {\color{red}2190}$.

Determine whether $2190$ is divisible by $2$.

It is divisible, thus, divide $2190$ by ${\color{green}2}$: $\frac{2190}{2} = {\color{red}1095}$.

Determine whether $1095$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1095$ is divisible by $3$.

It is divisible, thus, divide $1095$ by ${\color{green}3}$: $\frac{1095}{3} = {\color{red}365}$.

Determine whether $365$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $365$ is divisible by $5$.

It is divisible, thus, divide $365$ by ${\color{green}5}$: $\frac{365}{5} = {\color{red}73}$.

The prime number ${\color{green}73}$ has no other factors then $1$ and ${\color{green}73}$: $\frac{73}{73} = {\color{red}1}$.

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: $4380 = 2^{2} \cdot 3 \cdot 5 \cdot 73$.

The prime factorization is $4380 = 2^{2} \cdot 3 \cdot 5 \cdot 73$A.