# Prime factorization of $1862$

The calculator will find the prime factorization of $1862$, with steps shown.

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Find the prime factorization of $1862$.

### Solution

Start with the number $2$.

Determine whether $1862$ is divisible by $2$.

It is divisible, thus, divide $1862$ by ${\color{green}2}$: $\frac{1862}{2} = {\color{red}931}$.

Determine whether $931$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $931$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $931$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $931$ is divisible by $7$.

It is divisible, thus, divide $931$ by ${\color{green}7}$: $\frac{931}{7} = {\color{red}133}$.

Determine whether $133$ is divisible by $7$.

It is divisible, thus, divide $133$ by ${\color{green}7}$: $\frac{133}{7} = {\color{red}19}$.

The prime number ${\color{green}19}$ has no other factors then $1$ and ${\color{green}19}$: $\frac{19}{19} = {\color{red}1}$.

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: $1862 = 2 \cdot 7^{2} \cdot 19$.

The prime factorization is $1862 = 2 \cdot 7^{2} \cdot 19$A.