# Prime factorization of $1448$

The calculator will find the prime factorization of $1448$, with steps shown.

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Find the prime factorization of $1448$.

### Solution

Start with the number $2$.

Determine whether $1448$ is divisible by $2$.

It is divisible, thus, divide $1448$ by ${\color{green}2}$: $\frac{1448}{2} = {\color{red}724}$.

Determine whether $724$ is divisible by $2$.

It is divisible, thus, divide $724$ by ${\color{green}2}$: $\frac{724}{2} = {\color{red}362}$.

Determine whether $362$ is divisible by $2$.

It is divisible, thus, divide $362$ by ${\color{green}2}$: $\frac{362}{2} = {\color{red}181}$.

The prime number ${\color{green}181}$ has no other factors then $1$ and ${\color{green}181}$: $\frac{181}{181} = {\color{red}1}$.

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: $1448 = 2^{3} \cdot 181$.

The prime factorization is $1448 = 2^{3} \cdot 181$A.