# Prime factorization of $1450$

The calculator will find the prime factorization of $1450$, with steps shown.

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Find the prime factorization of $1450$.

### Solution

Start with the number $2$.

Determine whether $1450$ is divisible by $2$.

It is divisible, thus, divide $1450$ by ${\color{green}2}$: $\frac{1450}{2} = {\color{red}725}$.

Determine whether $725$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $725$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $725$ is divisible by $5$.

It is divisible, thus, divide $725$ by ${\color{green}5}$: $\frac{725}{5} = {\color{red}145}$.

Determine whether $145$ is divisible by $5$.

It is divisible, thus, divide $145$ by ${\color{green}5}$: $\frac{145}{5} = {\color{red}29}$.

The prime number ${\color{green}29}$ has no other factors then $1$ and ${\color{green}29}$: $\frac{29}{29} = {\color{red}1}$.

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: $1450 = 2 \cdot 5^{2} \cdot 29$.

The prime factorization is $1450 = 2 \cdot 5^{2} \cdot 29$A.