# Prime factorization of $1036$

The calculator will find the prime factorization of $1036$, with steps shown.

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Find the prime factorization of $1036$.

### Solution

Start with the number $2$.

Determine whether $1036$ is divisible by $2$.

It is divisible, thus, divide $1036$ by ${\color{green}2}$: $\frac{1036}{2} = {\color{red}518}$.

Determine whether $518$ is divisible by $2$.

It is divisible, thus, divide $518$ by ${\color{green}2}$: $\frac{518}{2} = {\color{red}259}$.

Determine whether $259$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $259$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $259$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $259$ is divisible by $7$.

It is divisible, thus, divide $259$ by ${\color{green}7}$: $\frac{259}{7} = {\color{red}37}$.

The prime number ${\color{green}37}$ has no other factors then $1$ and ${\color{green}37}$: $\frac{37}{37} = {\color{red}1}$.

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: $1036 = 2^{2} \cdot 7 \cdot 37$.

The prime factorization is $1036 = 2^{2} \cdot 7 \cdot 37$A.