Question

Express following number as the product of power of their prime factors $ 1024 $ .

Answer 1

Hint: To find the product of prime factors of any number we divide the given number with $ 2 $ and keep dividing it by $ 2 $ if it is possible. But, if it is not then to see if it is divisible by $ 3 $ , but if not then we try other numbers like $ 5,\,\,7 $ and so on till we get all possible prime factors of given number.

Complete step-by-step answer:
Given number is $ 1024 $
Finding prime factors of given number as follows:
 $ \begin{array}{*{20}{c}}
  2 & {1024} \\
\hline
  2 & {512} \\
\hline
  2 & {256} \\
\hline
  2 & {128} \\
\hline
  2 & {64} \\
\hline
  2 & {32} \\
\hline
  2 & {16} \\
\hline
  2 & 8 \\
\hline
  2 & 4 \\
\hline
  2 & 2 \\
\hline
  2 & 1
\end{array} $
Or we can write $ 1024 $ as \[2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\]
Since, prime factors of $ 1024 $ are all multiple of two’s.
And we know that number under multiplication with the same base power gets added.
Then from above we can write $ 1024 $ = $ {\left( 2 \right)^{1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1}} $
Or we can write as
 $ 1024 = {\left( 2 \right)^{10}} $
Which is the required power form of prime factor of number $ 1024 $ .

Note: While making prime factors of any number always start dividing it with $ 2 $ first and keep on until division is possible and when it is not possible then try others numbers like $ 3,\,\,5,\,\,7.... $ to find all prime factors of given number.