# Prime factorization of $3698$

The calculator will find the prime factorization of $3698$, with steps shown.

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Find the prime factorization of $3698$.

### Solution

Start with the number $2$.

Determine whether $3698$ is divisible by $2$.

It is divisible, thus, divide $3698$ by ${\color{green}2}$: $\frac{3698}{2} = {\color{red}1849}$.

Determine whether $1849$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1849$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1849$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1849$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $1849$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $1849$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $1849$ is divisible by $17$.

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

The next prime number is $19$.

Determine whether $1849$ is divisible by $19$.

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

The next prime number is $23$.

Determine whether $1849$ is divisible by $23$.

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

The next prime number is $29$.

Determine whether $1849$ is divisible by $29$.

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

The next prime number is $31$.

Determine whether $1849$ is divisible by $31$.

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

The next prime number is $37$.

Determine whether $1849$ is divisible by $37$.

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

The next prime number is $41$.

Determine whether $1849$ is divisible by $41$.

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

The next prime number is $43$.

Determine whether $1849$ is divisible by $43$.

It is divisible, thus, divide $1849$ by ${\color{green}43}$: $\frac{1849}{43} = {\color{red}43}$.

The prime number ${\color{green}43}$ has no other factors then $1$ and ${\color{green}43}$: $\frac{43}{43} = {\color{red}1}$.

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: $3698 = 2 \cdot 43^{2}$.

The prime factorization is $3698 = 2 \cdot 43^{2}$A.