# Prime factorization of $2274$

The calculator will find the prime factorization of $2274$, with steps shown.

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Find the prime factorization of $2274$.

### Solution

Start with the number $2$.

Determine whether $2274$ is divisible by $2$.

It is divisible, thus, divide $2274$ by ${\color{green}2}$: $\frac{2274}{2} = {\color{red}1137}$.

Determine whether $1137$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1137$ is divisible by $3$.

It is divisible, thus, divide $1137$ by ${\color{green}3}$: $\frac{1137}{3} = {\color{red}379}$.

The prime number ${\color{green}379}$ has no other factors then $1$ and ${\color{green}379}$: $\frac{379}{379} = {\color{red}1}$.

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: $2274 = 2 \cdot 3 \cdot 379$.

The prime factorization is $2274 = 2 \cdot 3 \cdot 379$A.