Question

Write all the factors of the following number.
24

Answer 1

Hint: We will be using the concept of number systems to solve the problem. We will be using the fact that factors of a number are numbers which completely divides the number.

Complete step-by-step solution -
Now, we have to find the all factors of 24.
Now, to find all the factors of 24. We have to find all the numbers which divide 24 completely. So, first we will write 24 in prime factorization as,
$\begin{align}
  & 24=1\times 2\times 3\times 2\times 2 \\
 & =1\times 2\times 2\times 2\times 3 \\
\end{align}$
Now, we will take different combinations of all the prime factors to get all the factors of 24.
So, first we have the number 24 itself. So, the one factor of 24 is 24 itself.
Also, we know that 1 divides all the numbers. Therefore, 1 is also a factor of 24.
Now, by taking different combinations of all prime factors of 24. We have the factors as,
\[\begin{align}
  & 1\times 2=2 \\
 & 1\times 2\times 2=4 \\
 & 1\times 2\times 2\times 2=8 \\
 & 2\times 3=6 \\
 & 2\times 2\times 3=12 \\
 & 1\times 3=3 \\
\end{align}\]
So, all the factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.

Note: To solve these types of questions one must know to factorize a number and find all its possible combinations which results in distinct factors. Also alternatively one can check from 2 to till the number itself, all the numbers for finding factors.