Question

What is the GCF of 4,12, and 28?

Answer 1

Hint: The GCF or the greatest common factor of a group of numbers can be found by listing the individual factors of each of the given numbers and then finding the factor which is common to all the numbers and which is the greatest in value among the other common factors.

Complete step by step answer:
In the question we are given the numbers, 4,12 and 28. First let us write down all the factors for each of the numbers. First, taking 4 and writing down its factors, we get,
$\begin{align}
  & 4=2\times 2 \\
 & 4=4\times 1 \\
\end{align}$
Hence, the factors of 4 are 1,2 and 4.
Next, find the factors of 12, we get,
$\begin{align}
  & 12=4\times 3 \\
 & 12=2\times 2\times 3 \\
 & 12=6\times 2 \\
 & 12=12\times 1 \\
\end{align}$
Hence, the factors of 12 are 1,2,3,4,6 and 12.
Next, find the factors of 28, we get,
$\begin{align}
  & 28=7\times 4 \\
 & 28=2\times 14 \\
 & 28=28\times 1 \\
\end{align}$
Hence, the factors of 28 are 1,2,4,7,14 and 28.
Finally, we can write down the common factors among the given 3 members. Clearly, the common factors are 1,2 and 4. Hence the GCF or the greatest common factor is the highest valued common factor which is 4.

Note: Another simple way to solve this problem is to check if the smallest number given is a factor of the other numbers, if this is true then we can conclude that the smallest number is the GCF for the given group of numbers. In this question we have 4,12 and 28. We can clearly see that 4 is a factor of both 12 and 28 and hence 4 is the GCF for the given group of numbers.