Question

Prime factors of $256$ are-

Answer 1

Hint: Within the problem we can observe the term ‘prime factors. We all know that prime factorization is the process of factoring a number with only using the prime numbers starting with $2$. So first we need to check whether the given number is divisible by $2$ or not. If the number is divisible $2$ then we can write the given number as a product of $2$ and the quotient. Now consider the quotient obtained and check whether it is divisible by $2$ or not. If it is divisible then also, we can write it as a product of factors. We will continue with the above process until we will get the quotient as $1$. While doing the above process if you get any number is not divisible by $2$, then check for the remaining prime numbers like $3$, $5$, $7$, $11...$.

Complete step by step solution:
Given number $256$.
Checking whether the number $256$ is divisible by $2$ or not. We can observe that the number $256$ is divisible by $2$ and the quotient will be $128$. Then we can write the number $256$ as
$256=2\times 128$
Now checking if the number $128$ is divisible by $2$ or not. We can observe that the number $128$ is divisible by $2$ and the quotient will be $64$. Then we can write the number $128$ as
$128=2\times 64$
From the above value we can write $256$ as
$256=2\times 2\times 64$
Now checking if the number $64$ is divisible by $2$ or not. We can observe that the number $64$ is divisible by $2$ and the quotient will be $32$. Then we can write the number $64$ as
$64=2\times 32$
From the above value we can write $256$ as
$256=2\times 2\times 2\times 32$
Now checking if the number $32$ is divisible by $2$ or not. We can observe that the number $32$ is divisible by $2$ and the quotient will be $16$. Then we can write the number $32$ as
$32=2\times 16$
From the above value we can write $256$ as
$256=2\times 2\times 2\times 2\times 16$
Now checking the number $16$ is divisible by $2$ or not. We can observe that the number $16$ is divisible by $2$ and the quotient will be $8$. Then we can write the number $16$ as
$16=2\times 8$
From the above value we can write $256$ as
$256=2\times 2\times 2\times 2\times 2\times 8$
Now checking if the number $8$ is divisible by $2$ or not. We can observe that the number $8$ is divisible by $2$ and the quotient will be $4$. Then we can write the number $8$ as
$8=2\times 4$
From the above value we can write $256$ as
$256=2\times 2\times 2\times 2\times 2\times 2\times 4$
Now checking if the number $4$ is divisible by $2$ or not. We can observe that the number $4$ is divisible by $2$ and the quotient will be $2$. Then we can write the number $4$ as
$4=2\times 2$
From the above value we can write $256$ as
$256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

In the above equation we can observe that only one factor is there for the number $256$ which is $2$.

Hence the prime factor of the number $256$ is $2$ only.

Note: In the problem they have mentioned prime factorization so we have checked that the given number is divisible by prime numbers or not only. If they have only mentioned factorization, then we need to check whether the given number is divisible by all the numbers.