Prime factorization of $$$1298$$$

Find the prime factorization of $$$1298$$$.

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

Determine whether $$$1298$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1298$$$ by $$${\color{green}2}$$$: $$$\frac{1298}{2} = {\color{red}649}$$$.

Determine whether $$$649$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$649$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$649$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$649$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$649$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$649$$$ by $$${\color{green}11}$$$: $$$\frac{649}{11} = {\color{red}59}$$$.

The prime number $$${\color{green}59}$$$ has no other factors then $$$1$$$ and $$${\color{green}59}$$$: $$$\frac{59}{59} = {\color{red}1}$$$.

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: $$$1298 = 2 \cdot 11 \cdot 59$$$.

The prime factorization is $$$1298 = 2 \cdot 11 \cdot 59$$$A.