Prime factorization of $$$3476$$$

Find the prime factorization of $$$3476$$$.

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

Determine whether $$$3476$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3476$$$ by $$${\color{green}2}$$$: $$$\frac{3476}{2} = {\color{red}1738}$$$.

Determine whether $$$1738$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1738$$$ by $$${\color{green}2}$$$: $$$\frac{1738}{2} = {\color{red}869}$$$.

Determine whether $$$869$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$869$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$869$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$869$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$869$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$869$$$ by $$${\color{green}11}$$$: $$$\frac{869}{11} = {\color{red}79}$$$.

The prime number $$${\color{green}79}$$$ has no other factors then $$$1$$$ and $$${\color{green}79}$$$: $$$\frac{79}{79} = {\color{red}1}$$$.

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: $$$3476 = 2^{2} \cdot 11 \cdot 79$$$.

The prime factorization is $$$3476 = 2^{2} \cdot 11 \cdot 79$$$A.