# Prime factorization of $1526$

The calculator will find the prime factorization of $1526$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $1526$.

### Solution

Start with the number $2$.

Determine whether $1526$ is divisible by $2$.

It is divisible, thus, divide $1526$ by ${\color{green}2}$: $\frac{1526}{2} = {\color{red}763}$.

Determine whether $763$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $763$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $763$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $763$ is divisible by $7$.

It is divisible, thus, divide $763$ by ${\color{green}7}$: $\frac{763}{7} = {\color{red}109}$.

The prime number ${\color{green}109}$ has no other factors then $1$ and ${\color{green}109}$: $\frac{109}{109} = {\color{red}1}$.

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: $1526 = 2 \cdot 7 \cdot 109$.

The prime factorization is $1526 = 2 \cdot 7 \cdot 109$A.