# Prime factorization of $3132$

The calculator will find the prime factorization of $3132$, with steps shown.

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Find the prime factorization of $3132$.

### Solution

Start with the number $2$.

Determine whether $3132$ is divisible by $2$.

It is divisible, thus, divide $3132$ by ${\color{green}2}$: $\frac{3132}{2} = {\color{red}1566}$.

Determine whether $1566$ is divisible by $2$.

It is divisible, thus, divide $1566$ by ${\color{green}2}$: $\frac{1566}{2} = {\color{red}783}$.

Determine whether $783$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $783$ is divisible by $3$.

It is divisible, thus, divide $783$ by ${\color{green}3}$: $\frac{783}{3} = {\color{red}261}$.

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: $3132 = 2^{2} \cdot 3^{3} \cdot 29$.

The prime factorization is $3132 = 2^{2} \cdot 3^{3} \cdot 29$A.