Prime factorization of $$$4756$$$

Find the prime factorization of $$$4756$$$.

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

Determine whether $$$4756$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4756$$$ by $$${\color{green}2}$$$: $$$\frac{4756}{2} = {\color{red}2378}$$$.

Determine whether $$$2378$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2378$$$ by $$${\color{green}2}$$$: $$$\frac{2378}{2} = {\color{red}1189}$$$.

Determine whether $$$1189$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1189$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1189$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1189$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$1189$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$1189$$$ is divisible by $$$13$$$.

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

The next prime number is $$$17$$$.

Determine whether $$$1189$$$ is divisible by $$$17$$$.

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

The next prime number is $$$19$$$.

Determine whether $$$1189$$$ is divisible by $$$19$$$.

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

The next prime number is $$$23$$$.

Determine whether $$$1189$$$ is divisible by $$$23$$$.

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

The next prime number is $$$29$$$.

Determine whether $$$1189$$$ is divisible by $$$29$$$.

It is divisible, thus, divide $$$1189$$$ by $$${\color{green}29}$$$: $$$\frac{1189}{29} = {\color{red}41}$$$.

The prime number $$${\color{green}41}$$$ has no other factors then $$$1$$$ and $$${\color{green}41}$$$: $$$\frac{41}{41} = {\color{red}1}$$$.

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: $$$4756 = 2^{2} \cdot 29 \cdot 41$$$.

The prime factorization is $$$4756 = 2^{2} \cdot 29 \cdot 41$$$A.