# Prime factorization of $4667$

The calculator will find the prime factorization of $4667$, with steps shown.

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Find the prime factorization of $4667$.

### Solution

Start with the number $2$.

Determine whether $4667$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4667$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $4667$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $4667$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $4667$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $4667$ is divisible by $13$.

It is divisible, thus, divide $4667$ by ${\color{green}13}$: $\frac{4667}{13} = {\color{red}359}$.

The prime number ${\color{green}359}$ has no other factors then $1$ and ${\color{green}359}$: $\frac{359}{359} = {\color{red}1}$.

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: $4667 = 13 \cdot 359$.

The prime factorization is $4667 = 13 \cdot 359$A.