# Prime factorization of $4263$

The calculator will find the prime factorization of $4263$, with steps shown.

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Find the prime factorization of $4263$.

### Solution

Start with the number $2$.

Determine whether $4263$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4263$ is divisible by $3$.

It is divisible, thus, divide $4263$ by ${\color{green}3}$: $\frac{4263}{3} = {\color{red}1421}$.

Determine whether $1421$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1421$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1421$ is divisible by $7$.

It is divisible, thus, divide $1421$ by ${\color{green}7}$: $\frac{1421}{7} = {\color{red}203}$.

Determine whether $203$ is divisible by $7$.

It is divisible, thus, divide $203$ by ${\color{green}7}$: $\frac{203}{7} = {\color{red}29}$.

The prime number ${\color{green}29}$ has no other factors then $1$ and ${\color{green}29}$: $\frac{29}{29} = {\color{red}1}$.

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: $4263 = 3 \cdot 7^{2} \cdot 29$.

The prime factorization is $4263 = 3 \cdot 7^{2} \cdot 29$A.