# Prime factorization of $152$

The calculator will find the prime factorization of $152$, with steps shown.

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Find the prime factorization of $152$.

### Solution

Start with the number $2$.

Determine whether $152$ is divisible by $2$.

It is divisible, thus, divide $152$ by ${\color{green}2}$: $\frac{152}{2} = {\color{red}76}$.

Determine whether $76$ is divisible by $2$.

It is divisible, thus, divide $76$ by ${\color{green}2}$: $\frac{76}{2} = {\color{red}38}$.

Determine whether $38$ is divisible by $2$.

It is divisible, thus, divide $38$ by ${\color{green}2}$: $\frac{38}{2} = {\color{red}19}$.

The prime number ${\color{green}19}$ has no other factors then $1$ and ${\color{green}19}$: $\frac{19}{19} = {\color{red}1}$.

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: $152 = 2^{3} \cdot 19$.

The prime factorization is $152 = 2^{3} \cdot 19$A.