# Prime factorization of $4122$

The calculator will find the prime factorization of $4122$, with steps shown.

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Find the prime factorization of $4122$.

### Solution

Start with the number $2$.

Determine whether $4122$ is divisible by $2$.

It is divisible, thus, divide $4122$ by ${\color{green}2}$: $\frac{4122}{2} = {\color{red}2061}$.

Determine whether $2061$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2061$ is divisible by $3$.

It is divisible, thus, divide $2061$ by ${\color{green}3}$: $\frac{2061}{3} = {\color{red}687}$.

Determine whether $687$ is divisible by $3$.

It is divisible, thus, divide $687$ by ${\color{green}3}$: $\frac{687}{3} = {\color{red}229}$.

The prime number ${\color{green}229}$ has no other factors then $1$ and ${\color{green}229}$: $\frac{229}{229} = {\color{red}1}$.

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: $4122 = 2 \cdot 3^{2} \cdot 229$.

The prime factorization is $4122 = 2 \cdot 3^{2} \cdot 229$A.