Prime factorization of $$$1364$$$

The calculator will find the prime factorization of $$$1364$$$, with steps shown.

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Your Input

Find the prime factorization of $$$1364$$$.

Solution

Start with the number $$$2$$$.

Determine whether $$$1364$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1364$$$ by $$${\color{green}2}$$$: $$$\frac{1364}{2} = {\color{red}682}$$$.

Determine whether $$$682$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$682$$$ by $$${\color{green}2}$$$: $$$\frac{682}{2} = {\color{red}341}$$$.

Determine whether $$$341$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$341$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$341$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$341$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$341$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$341$$$ by $$${\color{green}11}$$$: $$$\frac{341}{11} = {\color{red}31}$$$.

The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.

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: $$$1364 = 2^{2} \cdot 11 \cdot 31$$$.

Answer

The prime factorization is $$$1364 = 2^{2} \cdot 11 \cdot 31$$$A.