# Prime factorization of $3480$

The calculator will find the prime factorization of $3480$, with steps shown.

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Find the prime factorization of $3480$.

### Solution

Start with the number $2$.

Determine whether $3480$ is divisible by $2$.

It is divisible, thus, divide $3480$ by ${\color{green}2}$: $\frac{3480}{2} = {\color{red}1740}$.

Determine whether $1740$ is divisible by $2$.

It is divisible, thus, divide $1740$ by ${\color{green}2}$: $\frac{1740}{2} = {\color{red}870}$.

Determine whether $870$ is divisible by $2$.

It is divisible, thus, divide $870$ by ${\color{green}2}$: $\frac{870}{2} = {\color{red}435}$.

Determine whether $435$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $435$ is divisible by $3$.

It is divisible, thus, divide $435$ by ${\color{green}3}$: $\frac{435}{3} = {\color{red}145}$.

Determine whether $145$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $145$ is divisible by $5$.

It is divisible, thus, divide $145$ by ${\color{green}5}$: $\frac{145}{5} = {\color{red}29}$.

The prime number ${\color{green}29}$ has no other factors then $1$ and ${\color{green}29}$: $\frac{29}{29} = {\color{red}1}$.

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: $3480 = 2^{3} \cdot 3 \cdot 5 \cdot 29$.

The prime factorization is $3480 = 2^{3} \cdot 3 \cdot 5 \cdot 29$A.