Prime factorization of $$$1484$$$

Find the prime factorization of $$$1484$$$.

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

Determine whether $$$1484$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1484$$$ by $$${\color{green}2}$$$: $$$\frac{1484}{2} = {\color{red}742}$$$.

Determine whether $$$742$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$742$$$ by $$${\color{green}2}$$$: $$$\frac{742}{2} = {\color{red}371}$$$.

Determine whether $$$371$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$371$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$371$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$371$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$371$$$ by $$${\color{green}7}$$$: $$$\frac{371}{7} = {\color{red}53}$$$.

The prime number $$${\color{green}53}$$$ has no other factors then $$$1$$$ and $$${\color{green}53}$$$: $$$\frac{53}{53} = {\color{red}1}$$$.

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: $$$1484 = 2^{2} \cdot 7 \cdot 53$$$.

The prime factorization is $$$1484 = 2^{2} \cdot 7 \cdot 53$$$A.