Question

What is the GCF of 24 and 48?

Answer 1

Hint: Here in this question we have been asked to find the Greatest common factor of 24 and 48 for answering this question we will first find the common prime factors of 24 and 48 then we will multiply them and extract the greatest possible common factor.

Complete step-by-step solution:
Now considering from the question we have been asked to find the Greatest common factor of 24 and 48.
From the basic concepts we know that the greatest common factor of any two numbers can be obtained by list out all the factors of the given number and making note of the greatest among the common out of the list.
For obtaining the greatest common factor of the given numbers it would be easy to follow the prime factorization method.
 So firstly by prime factorization 24 we will get
$\begin{align}
  & 2\left| \!{\underline {\,
  24 \,}} \right. \\
 & 2\left| \!{\underline {\,
  12 \,}} \right. \\
 & 2\left| \!{\underline {\,
  6 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$ .
Hence we can say that the $24={{2}^{3}}\times 3$ .
Now by similarly factorization for 48 we will have ${{2}^{4}}\times 3$ .
Here the product of the common factors is ${{2}^{3}}\times 3=24$.
Therefore we can conclude that the greatest common factor of 24 and 48 is 24.

Note: In the process of answering questions of this type a very short span of time is required. Similarly we can find the least common multiple among them. Here by observing this we can come to a conclusion that when one number is a factor of the other then the greatest common factor of the two numbers will be the smallest number itself. Here 24 is the factor of 48 therefore 24 is the GCF.