Prime factorization of $$$676$$$

Find the prime factorization of $$$676$$$.

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

Determine whether $$$676$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$676$$$ by $$${\color{green}2}$$$: $$$\frac{676}{2} = {\color{red}338}$$$.

Determine whether $$$338$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$338$$$ by $$${\color{green}2}$$$: $$$\frac{338}{2} = {\color{red}169}$$$.

Determine whether $$$169$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$169$$$ by $$${\color{green}13}$$$: $$$\frac{169}{13} = {\color{red}13}$$$.

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: $$$676 = 2^{2} \cdot 13^{2}$$$.

The prime factorization is $$$676 = 2^{2} \cdot 13^{2}$$$A.