# Prime factorization of $$$1258$$$

### Your Input

**Find the prime factorization of $$$1258$$$.**

### Solution

Start with the number $$$2$$$.

Determine whether $$$1258$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1258$$$ by $$${\color{green}2}$$$: $$$\frac{1258}{2} = {\color{red}629}$$$.

Determine whether $$$629$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$629$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$629$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$629$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$629$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$629$$$ is divisible by $$$13$$$.

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

The next prime number is $$$17$$$.

Determine whether $$$629$$$ is divisible by $$$17$$$.

It is divisible, thus, divide $$$629$$$ by $$${\color{green}17}$$$: $$$\frac{629}{17} = {\color{red}37}$$$.

The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.

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: $$$1258 = 2 \cdot 17 \cdot 37$$$.

### Answer

**The prime factorization is $$$1258 = 2 \cdot 17 \cdot 37$$$A.**