# Prime factorization of $4004$

The calculator will find the prime factorization of $4004$, with steps shown.

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Find the prime factorization of $4004$.

### Solution

Start with the number $2$.

Determine whether $4004$ is divisible by $2$.

It is divisible, thus, divide $4004$ by ${\color{green}2}$: $\frac{4004}{2} = {\color{red}2002}$.

Determine whether $2002$ is divisible by $2$.

It is divisible, thus, divide $2002$ by ${\color{green}2}$: $\frac{2002}{2} = {\color{red}1001}$.

Determine whether $1001$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1001$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1001$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1001$ is divisible by $7$.

It is divisible, thus, divide $1001$ by ${\color{green}7}$: $\frac{1001}{7} = {\color{red}143}$.

Determine whether $143$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $143$ is divisible by $11$.

It is divisible, thus, divide $143$ by ${\color{green}11}$: $\frac{143}{11} = {\color{red}13}$.

The prime number ${\color{green}13}$ has no other factors then $1$ and ${\color{green}13}$: $\frac{13}{13} = {\color{red}1}$.

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: $4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13$.

The prime factorization is $4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13$A.