Prime factorization of $$$2961$$$

Find the prime factorization of $$$2961$$$.

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

Determine whether $$$2961$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2961$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2961$$$ by $$${\color{green}3}$$$: $$$\frac{2961}{3} = {\color{red}987}$$$.

Determine whether $$$987$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$987$$$ by $$${\color{green}3}$$$: $$$\frac{987}{3} = {\color{red}329}$$$.

Determine whether $$$329$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$329$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$329$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$329$$$ by $$${\color{green}7}$$$: $$$\frac{329}{7} = {\color{red}47}$$$.

The prime number $$${\color{green}47}$$$ has no other factors then $$$1$$$ and $$${\color{green}47}$$$: $$$\frac{47}{47} = {\color{red}1}$$$.

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: $$$2961 = 3^{2} \cdot 7 \cdot 47$$$.

The prime factorization is $$$2961 = 3^{2} \cdot 7 \cdot 47$$$A.