# Prime factorization of $4116$

The calculator will find the prime factorization of $4116$, with steps shown.

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Find the prime factorization of $4116$.

### Solution

Start with the number $2$.

Determine whether $4116$ is divisible by $2$.

It is divisible, thus, divide $4116$ by ${\color{green}2}$: $\frac{4116}{2} = {\color{red}2058}$.

Determine whether $2058$ is divisible by $2$.

It is divisible, thus, divide $2058$ by ${\color{green}2}$: $\frac{2058}{2} = {\color{red}1029}$.

Determine whether $1029$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1029$ is divisible by $3$.

It is divisible, thus, divide $1029$ by ${\color{green}3}$: $\frac{1029}{3} = {\color{red}343}$.

Determine whether $343$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $343$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $343$ is divisible by $7$.

It is divisible, thus, divide $343$ by ${\color{green}7}$: $\frac{343}{7} = {\color{red}49}$.

Determine whether $49$ is divisible by $7$.

It is divisible, thus, divide $49$ by ${\color{green}7}$: $\frac{49}{7} = {\color{red}7}$.

The prime number ${\color{green}7}$ has no other factors then $1$ and ${\color{green}7}$: $\frac{7}{7} = {\color{red}1}$.

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: $4116 = 2^{2} \cdot 3 \cdot 7^{3}$.

The prime factorization is $4116 = 2^{2} \cdot 3 \cdot 7^{3}$A.