# Prime factorization of $1484$

The calculator will find the prime factorization of $1484$, with steps shown.

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Find the prime factorization of $1484$.

### Solution

Start with the number $2$.

Determine whether $1484$ is divisible by $2$.

It is divisible, thus, divide $1484$ by ${\color{green}2}$: $\frac{1484}{2} = {\color{red}742}$.

Determine whether $742$ is divisible by $2$.

It is divisible, thus, divide $742$ by ${\color{green}2}$: $\frac{742}{2} = {\color{red}371}$.

Determine whether $371$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $371$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $371$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $371$ is divisible by $7$.

It is divisible, thus, divide $371$ by ${\color{green}7}$: $\frac{371}{7} = {\color{red}53}$.

The prime number ${\color{green}53}$ has no other factors then $1$ and ${\color{green}53}$: $\frac{53}{53} = {\color{red}1}$.

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: $1484 = 2^{2} \cdot 7 \cdot 53$.

The prime factorization is $1484 = 2^{2} \cdot 7 \cdot 53$A.