Question

How do you find the greatest common factor of 88, 55?

Answer 1

Hint: We are given the terms as 88 and 55 and we are asked to find the greatest common factor. We will first learn what the greatest factor means. Then we will learn about the possible technique that is there to help us in finding the greatest common factor. We will use the prime factorization method. We will factor 55 and 88 and look for the greatest term that is the same. In both the digits, we will grab those terms and the product of all such terms will be our answer.

Complete step-by-step solution:
We are given two terms as 88 and 55. We are asked to find the greatest common factor. We will learn what the greatest common factor means. Now, the greatest common factor means the greatest or the largest possible term that is common to the terms given to us. It is also known as HCF (Highest – Common Factor). We have 55 and 88 and we have to find the numbers which are common to 55 and 88. To find the HCF or the greatest common factor, we have different ways.
1. Factor Method
2. Long Division Method
We will find our answer using both methods to learn more methods. First, we will use Factor Method.
In this method, we will write the given term into its prime factor and then look for all possible common terms. Then we will club them and the product of these will be our HCF or the greatest common factor. We know 55 is written as the product of 5 and 11 while 88 is the product of \[11\times 2\times 2\times 2.\] So, we get,
\[\begin{align}
  & 55=5\times 11 \\
 & 88=2\times 11\times 2\times 2 \\
\end{align}\]
We can see that 11 is the term that is common to both 55 and 88. So, the HCF of 88 and 55 is 11.
Now we will find the greatest common factor using the long division method. So, we divide the term until the remainder is 0. Now, we get,
\[55\overset{1}{\overline{\left){\begin{align}
  & 88 \\
 & \underline{55} \\
 & 33 \\
\end{align}}\right.}}\]
\[33\overset{1}{\overline{\left){\begin{align}
  & 55 \\
 & \underline{33} \\
 & 22 \\
\end{align}}\right.}}\]
\[22\overset{1}{\overline{\left){\begin{align}
  & 33 \\
 & \underline{22} \\
 & 11 \\
\end{align}}\right.}}\]
\[11\overset{2}{\overline{\left){\begin{align}
  & 22 \\
 & \underline{22} \\
 & 0 \\
\end{align}}\right.}}\]
Therefore, HCF is 11.

Note: While finding the greatest common factor, we must factor into the prime factor only, then we can find the correct answer. If we do not find the prime factor, the answer will not be visible. For example, \[8=4\times 2\] and \[16=8\times 2.\] So we can see only 2 is common. So, the common term, one can assume as 2. And it will become an incorrect option or answer.