# Prime factorization of $3653$

The calculator will find the prime factorization of $3653$, with steps shown.

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Find the prime factorization of $3653$.

### Solution

Start with the number $2$.

Determine whether $3653$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3653$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $3653$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $3653$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $3653$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $3653$ is divisible by $13$.

It is divisible, thus, divide $3653$ by ${\color{green}13}$: $\frac{3653}{13} = {\color{red}281}$.

The prime number ${\color{green}281}$ has no other factors then $1$ and ${\color{green}281}$: $\frac{281}{281} = {\color{red}1}$.

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: $3653 = 13 \cdot 281$.

The prime factorization is $3653 = 13 \cdot 281$A.