# Prime factorization of $1400$

The calculator will find the prime factorization of $1400$, with steps shown.

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Find the prime factorization of $1400$.

### Solution

Start with the number $2$.

Determine whether $1400$ is divisible by $2$.

It is divisible, thus, divide $1400$ by ${\color{green}2}$: $\frac{1400}{2} = {\color{red}700}$.

Determine whether $700$ is divisible by $2$.

It is divisible, thus, divide $700$ by ${\color{green}2}$: $\frac{700}{2} = {\color{red}350}$.

Determine whether $350$ is divisible by $2$.

It is divisible, thus, divide $350$ by ${\color{green}2}$: $\frac{350}{2} = {\color{red}175}$.

Determine whether $175$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $175$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $175$ is divisible by $5$.

It is divisible, thus, divide $175$ by ${\color{green}5}$: $\frac{175}{5} = {\color{red}35}$.

Determine whether $35$ is divisible by $5$.

It is divisible, thus, divide $35$ by ${\color{green}5}$: $\frac{35}{5} = {\color{red}7}$.

The prime number ${\color{green}7}$ has no other factors then $1$ and ${\color{green}7}$: $\frac{7}{7} = {\color{red}1}$.

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: $1400 = 2^{3} \cdot 5^{2} \cdot 7$.

The prime factorization is $1400 = 2^{3} \cdot 5^{2} \cdot 7$A.