# Prime factorization of $1464$

The calculator will find the prime factorization of $1464$, with steps shown.

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Find the prime factorization of $1464$.

### Solution

Start with the number $2$.

Determine whether $1464$ is divisible by $2$.

It is divisible, thus, divide $1464$ by ${\color{green}2}$: $\frac{1464}{2} = {\color{red}732}$.

Determine whether $732$ is divisible by $2$.

It is divisible, thus, divide $732$ by ${\color{green}2}$: $\frac{732}{2} = {\color{red}366}$.

Determine whether $366$ is divisible by $2$.

It is divisible, thus, divide $366$ by ${\color{green}2}$: $\frac{366}{2} = {\color{red}183}$.

Determine whether $183$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $183$ is divisible by $3$.

It is divisible, thus, divide $183$ by ${\color{green}3}$: $\frac{183}{3} = {\color{red}61}$.

The prime number ${\color{green}61}$ has no other factors then $1$ and ${\color{green}61}$: $\frac{61}{61} = {\color{red}1}$.

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: $1464 = 2^{3} \cdot 3 \cdot 61$.

The prime factorization is $1464 = 2^{3} \cdot 3 \cdot 61$A.