Prime factorization of $$$1400$$$

Find the prime factorization of $$$1400$$$.

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

Determine whether $$$1400$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1400$$$ by $$${\color{green}2}$$$: $$$\frac{1400}{2} = {\color{red}700}$$$.

Determine whether $$$700$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$700$$$ by $$${\color{green}2}$$$: $$$\frac{700}{2} = {\color{red}350}$$$.

Determine whether $$$350$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$350$$$ by $$${\color{green}2}$$$: $$$\frac{350}{2} = {\color{red}175}$$$.

Determine whether $$$175$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$175$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$175$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$175$$$ by $$${\color{green}5}$$$: $$$\frac{175}{5} = {\color{red}35}$$$.

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: $$$1400 = 2^{3} \cdot 5^{2} \cdot 7$$$.

The prime factorization is $$$1400 = 2^{3} \cdot 5^{2} \cdot 7$$$A.