Prime factorization of $$$1434$$$

Find the prime factorization of $$$1434$$$.

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

Determine whether $$$1434$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1434$$$ by $$${\color{green}2}$$$: $$$\frac{1434}{2} = {\color{red}717}$$$.

Determine whether $$$717$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$717$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$717$$$ by $$${\color{green}3}$$$: $$$\frac{717}{3} = {\color{red}239}$$$.

The prime number $$${\color{green}239}$$$ has no other factors then $$$1$$$ and $$${\color{green}239}$$$: $$$\frac{239}{239} = {\color{red}1}$$$.

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: $$$1434 = 2 \cdot 3 \cdot 239$$$.

The prime factorization is $$$1434 = 2 \cdot 3 \cdot 239$$$A.