# Prime factorization of $3624$

The calculator will find the prime factorization of $3624$, with steps shown.

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Find the prime factorization of $3624$.

### Solution

Start with the number $2$.

Determine whether $3624$ is divisible by $2$.

It is divisible, thus, divide $3624$ by ${\color{green}2}$: $\frac{3624}{2} = {\color{red}1812}$.

Determine whether $1812$ is divisible by $2$.

It is divisible, thus, divide $1812$ by ${\color{green}2}$: $\frac{1812}{2} = {\color{red}906}$.

Determine whether $906$ is divisible by $2$.

It is divisible, thus, divide $906$ by ${\color{green}2}$: $\frac{906}{2} = {\color{red}453}$.

Determine whether $453$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $453$ is divisible by $3$.

It is divisible, thus, divide $453$ by ${\color{green}3}$: $\frac{453}{3} = {\color{red}151}$.

The prime number ${\color{green}151}$ has no other factors then $1$ and ${\color{green}151}$: $\frac{151}{151} = {\color{red}1}$.

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: $3624 = 2^{3} \cdot 3 \cdot 151$.

The prime factorization is $3624 = 2^{3} \cdot 3 \cdot 151$A.