Prime factorization of $$$1849$$$

Find the prime factorization of $$$1849$$$.

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

Determine whether $$$1849$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1849$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1849$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1849$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$1849$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$1849$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$1849$$$ is divisible by $$$17$$$.

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

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

Determine whether $$$1849$$$ is divisible by $$$19$$$.

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

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

Determine whether $$$1849$$$ is divisible by $$$23$$$.

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

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

Determine whether $$$1849$$$ is divisible by $$$29$$$.

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

The next prime number is $$$31$$$.

Determine whether $$$1849$$$ is divisible by $$$31$$$.

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

The next prime number is $$$37$$$.

Determine whether $$$1849$$$ is divisible by $$$37$$$.

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

The next prime number is $$$41$$$.

Determine whether $$$1849$$$ is divisible by $$$41$$$.

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

The next prime number is $$$43$$$.

Determine whether $$$1849$$$ is divisible by $$$43$$$.

It is divisible, thus, divide $$$1849$$$ by $$${\color{green}43}$$$: $$$\frac{1849}{43} = {\color{red}43}$$$.

The prime number $$${\color{green}43}$$$ has no other factors then $$$1$$$ and $$${\color{green}43}$$$: $$$\frac{43}{43} = {\color{red}1}$$$.

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: $$$1849 = 43^{2}$$$.

The prime factorization is $$$1849 = 43^{2}$$$A.