Prime factorization of $$$3136$$$

Find the prime factorization of $$$3136$$$.

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

Determine whether $$$3136$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3136$$$ by $$${\color{green}2}$$$: $$$\frac{3136}{2} = {\color{red}1568}$$$.

Determine whether $$$1568$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1568$$$ by $$${\color{green}2}$$$: $$$\frac{1568}{2} = {\color{red}784}$$$.

Determine whether $$$784$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$784$$$ by $$${\color{green}2}$$$: $$$\frac{784}{2} = {\color{red}392}$$$.

Determine whether $$$392$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$392$$$ by $$${\color{green}2}$$$: $$$\frac{392}{2} = {\color{red}196}$$$.

Determine whether $$$196$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$196$$$ by $$${\color{green}2}$$$: $$$\frac{196}{2} = {\color{red}98}$$$.

Determine whether $$$98$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$98$$$ by $$${\color{green}2}$$$: $$$\frac{98}{2} = {\color{red}49}$$$.

Determine whether $$$49$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$49$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$49$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$49$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$49$$$ by $$${\color{green}7}$$$: $$$\frac{49}{7} = {\color{red}7}$$$.

The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.

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: $$$3136 = 2^{6} \cdot 7^{2}$$$.

The prime factorization is $$$3136 = 2^{6} \cdot 7^{2}$$$A.