Question

How do you find the greatest common factor of 68, 34?

Answer 1

Hint: In order to find the greatest common factor, we must first find all the factors of the two given numbers by factoring the two numbers separately. Then we will look upon the factors which are common to both the numbers. Further, the greatest of all the factors will be termed as the greatest common factor of the given numbers.

Complete step-by-step solution:
The factors of 68 are given as:
$\begin{align}
  & 2\left| \!{\underline {\,
  68 \,}} \right. \\
 & 2\left| \!{\underline {\,
  34 \,}} \right. \\
 & 17\left| \!{\underline {\,
  17 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
Since, we know that a number is a factor of itself as well, thus 68 is a factor of 68 also.
Therefore, the factors of 68 are 1, 2, 17 and 68.
Now, the factors of 34 are given as:
$\begin{align}
  & 2\left| \!{\underline {\,
  34 \,}} \right. \\
 & 17\left| \!{\underline {\,
  17 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
Therefore, the factors of 34 are 1, 2, 17 and 34.
The common factors of 68 and 34 are 1, 2 and 17.
We know that the greatest number of all these three numbers is 17.
Therefore, we get that the greatest common factor of 68 and 34 is 17.

Note: We must be quick with our multiplicative skills to perform the factorization of greater numbers. During finding the factors of various numbers, we can often get confused during multiplication when there are a large number of factors to a number. One way to avoid this confusion is by step by step breaking down the number into a smaller number by dividing it by the prime numbers such as 2, 3 and 5 only during the factorization process.