# Prime factorization of $3878$

The calculator will find the prime factorization of $3878$, with steps shown.

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Find the prime factorization of $3878$.

### Solution

Start with the number $2$.

Determine whether $3878$ is divisible by $2$.

It is divisible, thus, divide $3878$ by ${\color{green}2}$: $\frac{3878}{2} = {\color{red}1939}$.

Determine whether $1939$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1939$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1939$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1939$ is divisible by $7$.

It is divisible, thus, divide $1939$ by ${\color{green}7}$: $\frac{1939}{7} = {\color{red}277}$.

The prime number ${\color{green}277}$ has no other factors then $1$ and ${\color{green}277}$: $\frac{277}{277} = {\color{red}1}$.

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: $3878 = 2 \cdot 7 \cdot 277$.

The prime factorization is $3878 = 2 \cdot 7 \cdot 277$A.