Prime factorization of $$$140$$$

Find the prime factorization of $$$140$$$.

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

Determine whether $$$140$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$140$$$ by $$${\color{green}2}$$$: $$$\frac{140}{2} = {\color{red}70}$$$.

Determine whether $$$70$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$70$$$ by $$${\color{green}2}$$$: $$$\frac{70}{2} = {\color{red}35}$$$.

Determine whether $$$35$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$35$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$35$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$35$$$ by $$${\color{green}5}$$$: $$$\frac{35}{5} = {\color{red}7}$$$.

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: $$$140 = 2^{2} \cdot 5 \cdot 7$$$.

The prime factorization is $$$140 = 2^{2} \cdot 5 \cdot 7$$$A.