# Prime factorization of $4176$

The calculator will find the prime factorization of $4176$, with steps shown.

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Find the prime factorization of $4176$.

### Solution

Start with the number $2$.

Determine whether $4176$ is divisible by $2$.

It is divisible, thus, divide $4176$ by ${\color{green}2}$: $\frac{4176}{2} = {\color{red}2088}$.

Determine whether $2088$ is divisible by $2$.

It is divisible, thus, divide $2088$ by ${\color{green}2}$: $\frac{2088}{2} = {\color{red}1044}$.

Determine whether $1044$ is divisible by $2$.

It is divisible, thus, divide $1044$ by ${\color{green}2}$: $\frac{1044}{2} = {\color{red}522}$.

Determine whether $522$ is divisible by $2$.

It is divisible, thus, divide $522$ by ${\color{green}2}$: $\frac{522}{2} = {\color{red}261}$.

Determine whether $261$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $261$ is divisible by $3$.

It is divisible, thus, divide $261$ by ${\color{green}3}$: $\frac{261}{3} = {\color{red}87}$.

Determine whether $87$ is divisible by $3$.

It is divisible, thus, divide $87$ by ${\color{green}3}$: $\frac{87}{3} = {\color{red}29}$.

The prime number ${\color{green}29}$ has no other factors then $1$ and ${\color{green}29}$: $\frac{29}{29} = {\color{red}1}$.

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: $4176 = 2^{4} \cdot 3^{2} \cdot 29$.

The prime factorization is $4176 = 2^{4} \cdot 3^{2} \cdot 29$A.