# Prime factorization of $1232$

The calculator will find the prime factorization of $1232$, with steps shown.

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Find the prime factorization of $1232$.

### Solution

Start with the number $2$.

Determine whether $1232$ is divisible by $2$.

It is divisible, thus, divide $1232$ by ${\color{green}2}$: $\frac{1232}{2} = {\color{red}616}$.

Determine whether $616$ is divisible by $2$.

It is divisible, thus, divide $616$ by ${\color{green}2}$: $\frac{616}{2} = {\color{red}308}$.

Determine whether $308$ is divisible by $2$.

It is divisible, thus, divide $308$ by ${\color{green}2}$: $\frac{308}{2} = {\color{red}154}$.

Determine whether $154$ is divisible by $2$.

It is divisible, thus, divide $154$ by ${\color{green}2}$: $\frac{154}{2} = {\color{red}77}$.

Determine whether $77$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $77$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $77$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $77$ is divisible by $7$.

It is divisible, thus, divide $77$ by ${\color{green}7}$: $\frac{77}{7} = {\color{red}11}$.

The prime number ${\color{green}11}$ has no other factors then $1$ and ${\color{green}11}$: $\frac{11}{11} = {\color{red}1}$.

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: $1232 = 2^{4} \cdot 7 \cdot 11$.

The prime factorization is $1232 = 2^{4} \cdot 7 \cdot 11$A.