# Prime factorization of $4950$

The calculator will find the prime factorization of $4950$, with steps shown.

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Find the prime factorization of $4950$.

### Solution

Start with the number $2$.

Determine whether $4950$ is divisible by $2$.

It is divisible, thus, divide $4950$ by ${\color{green}2}$: $\frac{4950}{2} = {\color{red}2475}$.

Determine whether $2475$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2475$ is divisible by $3$.

It is divisible, thus, divide $2475$ by ${\color{green}3}$: $\frac{2475}{3} = {\color{red}825}$.

Determine whether $825$ is divisible by $3$.

It is divisible, thus, divide $825$ by ${\color{green}3}$: $\frac{825}{3} = {\color{red}275}$.

Determine whether $275$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $275$ is divisible by $5$.

It is divisible, thus, divide $275$ by ${\color{green}5}$: $\frac{275}{5} = {\color{red}55}$.

Determine whether $55$ is divisible by $5$.

It is divisible, thus, divide $55$ by ${\color{green}5}$: $\frac{55}{5} = {\color{red}11}$.

The prime number ${\color{green}11}$ has no other factors then $1$ and ${\color{green}11}$: $\frac{11}{11} = {\color{red}1}$.

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: $4950 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 11$.

The prime factorization is $4950 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 11$A.