# Prime factorization of $1652$

The calculator will find the prime factorization of $1652$, with steps shown.

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Find the prime factorization of $1652$.

### Solution

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.