Question

The prime factor of 128 is
a. 0
b. 1
c. 2
d. 3

Answer 1

Hint: We will take reference from the basic definition of prime number to find the prime factor of the number 128. We will use the division method to find the prime factors of 128 and then select the best possible option.

Complete step-by-step answer:

It is given in this question that we have to find the prime factor of the number 128. To solve this question, we need to know what prime factor means. So, the prime factor is any prime number that can be multiplied to give the original number. And we know that prime numbers are those numbers which have only factors, that is 1 and the number itself. Examples for prime numbers are 2, 3, 5, 7, 11, etc.
Now, we will first find all the possible prime factors of 128, then identify the prime number among all the factors. We can find the prime factors by the division method as follows.
$\begin{align}
  & 2\left| \!{\underline {\,
  128 \,}} \right. \\
 & 2\left| \!{\underline {\,
  64 \,}} \right. \\
 & 2\left| \!{\underline {\,
  32 \,}} \right. \\
 & 2\left| \!{\underline {\,
  16 \,}} \right. \\
 & 2\left| \!{\underline {\,
  8 \,}} \right. \\
 & 2\left| \!{\underline {\,
  4 \,}} \right. \\
 & 2\left| \!{\underline {\,
  2 \,}} \right. \\
 & \text{ }1 \\
\end{align}$
We can also write 128 as $2\times 2\times 2\times 2\times 2\times 2\times 2$.
Now, we will look at the given options, so we can say that,
Option (a), 0 is incorrect because 0 is not a prime number.
Option (b), 1 is incorrect because 1 is not a prime number.
Option (c), 2 is the correct option because 2 is a prime number and also 2 is a factor of 128.
Option (d), 3 is an incorrect option because all though 3 is a prime number, it is not a factor of 128.
Therefore, we can say that option (c) is the correct answer.

Note: Many students may make mistakes while selecting the option. They might assume that 1 is a prime number as 1 divides 128 but this is wrong. As we know that 1 is not a prime number because 1 has only 1 factor. And the smallest prime factor is 2. Thus to avoid such mistakes, we have to keep in mind the basic definition of prime number.