# Prime factorization of $140$

The calculator will find the prime factorization of $140$, with steps shown.

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Find the prime factorization of $140$.

### Solution

Start with the number $2$.

Determine whether $140$ is divisible by $2$.

It is divisible, thus, divide $140$ by ${\color{green}2}$: $\frac{140}{2} = {\color{red}70}$.

Determine whether $70$ is divisible by $2$.

It is divisible, thus, divide $70$ by ${\color{green}2}$: $\frac{70}{2} = {\color{red}35}$.

Determine whether $35$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $35$ is divisible by $3$.

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

The next prime number is $5$.

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: $140 = 2^{2} \cdot 5 \cdot 7$.

The prime factorization is $140 = 2^{2} \cdot 5 \cdot 7$A.