Question

What is the GCF of 21 and 63?

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, 21 and 63. First let us write down all the factors for each of the numbers. First, taking 21 and writing down its factors, we get,
$\begin{align}
  & 21=3\times 7 \\
 & 21=21\times 1 \\
\end{align}$
Hence, the factors of 21 are 1,3,7 and 21.
Next, find the factors of 63, we get,
$\begin{align}
  & 63=21\times 3 \\
 & 63=7\times 3\times 3 \\
 & 63=63\times 1 \\
\end{align}$
Hence, the factors of 63 are 1,3,7,21 and 63.
Finally, we can write down the common factors among the given 2 members. Clearly, the common factors are 1,3,7 and 21. Hence the GCF or the greatest common factor is the highest valued common factor which is 21.

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 21 and 63. We can clearly see that 21 is a factor of 63 and hence 21 is the GCF for the given group of numbers.