# Prime factorization of $4949$

The calculator will find the prime factorization of $4949$, with steps shown.

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Find the prime factorization of $4949$.

### Solution

Start with the number $2$.

Determine whether $4949$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4949$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $4949$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $4949$ is divisible by $7$.

It is divisible, thus, divide $4949$ by ${\color{green}7}$: $\frac{4949}{7} = {\color{red}707}$.

Determine whether $707$ is divisible by $7$.

It is divisible, thus, divide $707$ by ${\color{green}7}$: $\frac{707}{7} = {\color{red}101}$.

The prime number ${\color{green}101}$ has no other factors then $1$ and ${\color{green}101}$: $\frac{101}{101} = {\color{red}1}$.

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: $4949 = 7^{2} \cdot 101$.

The prime factorization is $4949 = 7^{2} \cdot 101$A.