Question

What are the factors of $128$ ?

Answer 1

Hint: Here we will find the factor of given number by that number which divides the given number completely and leaves no remainder.

Complete step-by-step answer:
The factor of a number is that number which divides the given number completely. That leaves no remainder. To find the factors of number $128$, we will have to perform division on $128$ and find the numbers which divide $128$completely, leaving no remainder.
All the divisors which give remainder $0$ for our number $128$are the factors of $128$.
To calculate the factors of any number, here is $128$, we need to find all the numbers that would divide$128$ without leaving any remainder, we start with the number $1$ , then check for numbers $2,3,4,5,6,7,...$ etc up to $64$ (half of $128$)
The number $1$ and the number itself would always be the factors of the given number.
Proceeding like this way we get,
Hence the factors of $128$are $1,2,4,8,16,32,64,128$

Note: Prime factorization of a number refers to breaking down a number into the form of products of its prime factors. There are different methods that can be used to find the prime factorization of a number and hence its prime factors. To find prime factors of $128$using the division method.
Start dividing $128$from the smallest prime number. After finding the smallest prime factor of the number $128$that is $2$ divided by$128$we obtain the quotient $64$. Repeating this process we obtain the following,
$\begin{array}{*{20}{c}}
  {2\left| \!{\underline {\,
  {128} \,}} \right. } \\
  {2\left| \!{\underline {\,
  {64} \,}} \right. } \\
  {2\left| \!{\underline {\,
  {32} \,}} \right. } \\
  {2\left| \!{\underline {\,
  {16} \,}} \right. } \\
  {2\left| \!{\underline {\,
  4 \,}} \right. } \\
  {2\left| \!{\underline {\,
  2 \,}} \right. } \\
  {\underline 1 }
\end{array}$
So the prime factorization of $128$is $128 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = {2^7}$
Further find the products of the multiplicands in different orders to obtain the composite factors of the number. Thus the total factors can be written including booth the prime and composite numbers together as $1,2,4,8,16,32,64,128$