Prime factorization of $$$1652$$$

Find the prime factorization of $$$1652$$$.

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

Determine whether $$$1652$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1652$$$ by $$${\color{green}2}$$$: $$$\frac{1652}{2} = {\color{red}826}$$$.

Determine whether $$$826$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$826$$$ by $$${\color{green}2}$$$: $$$\frac{826}{2} = {\color{red}413}$$$.

Determine whether $$$413$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$413$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$413$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$413$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$413$$$ by $$${\color{green}7}$$$: $$$\frac{413}{7} = {\color{red}59}$$$.

The prime number $$${\color{green}59}$$$ has no other factors then $$$1$$$ and $$${\color{green}59}$$$: $$$\frac{59}{59} = {\color{red}1}$$$.

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: $$$1652 = 2^{2} \cdot 7 \cdot 59$$$.

The prime factorization is $$$1652 = 2^{2} \cdot 7 \cdot 59$$$A.