Prime factorization of $$$4294$$$

Find the prime factorization of $$$4294$$$.

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

Determine whether $$$4294$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4294$$$ by $$${\color{green}2}$$$: $$$\frac{4294}{2} = {\color{red}2147}$$$.

Determine whether $$$2147$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2147$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2147$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2147$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$2147$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$2147$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$2147$$$ is divisible by $$$17$$$.

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

The next prime number is $$$19$$$.

Determine whether $$$2147$$$ is divisible by $$$19$$$.

It is divisible, thus, divide $$$2147$$$ by $$${\color{green}19}$$$: $$$\frac{2147}{19} = {\color{red}113}$$$.

The prime number $$${\color{green}113}$$$ has no other factors then $$$1$$$ and $$${\color{green}113}$$$: $$$\frac{113}{113} = {\color{red}1}$$$.

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: $$$4294 = 2 \cdot 19 \cdot 113$$$.

The prime factorization is $$$4294 = 2 \cdot 19 \cdot 113$$$A.