# Prime factorization of $4476$

The calculator will find the prime factorization of $4476$, with steps shown.

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Find the prime factorization of $4476$.

### Solution

Start with the number $2$.

Determine whether $4476$ is divisible by $2$.

It is divisible, thus, divide $4476$ by ${\color{green}2}$: $\frac{4476}{2} = {\color{red}2238}$.

Determine whether $2238$ is divisible by $2$.

It is divisible, thus, divide $2238$ by ${\color{green}2}$: $\frac{2238}{2} = {\color{red}1119}$.

Determine whether $1119$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1119$ is divisible by $3$.

It is divisible, thus, divide $1119$ by ${\color{green}3}$: $\frac{1119}{3} = {\color{red}373}$.

The prime number ${\color{green}373}$ has no other factors then $1$ and ${\color{green}373}$: $\frac{373}{373} = {\color{red}1}$.

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: $4476 = 2^{2} \cdot 3 \cdot 373$.

The prime factorization is $4476 = 2^{2} \cdot 3 \cdot 373$A.