Question

How do you find the greatest common factor of 9,45?

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 answer:
Complete step-by-step solution:
The factors of 9 are given as:
$\begin{align}
  & 3\left| \!{\underline {\,
  9 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
Since, we know that a number is a factor of itself as well, thus 9 is a factor of 9 also.
Therefore, the factors of 9 are 1, 3 and 9.
Now, the factors of 45 are given as:
$\begin{align}
  & 3\left| \!{\underline {\,
  45 \,}} \right. \\
 & 3\left| \!{\underline {\,
  15 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
Or it can also be expressed as:
$\begin{align}
  & 9\left| \!{\underline {\,
  45 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
Therefore, the factors of 45 are 1, 3, 5, 9 and 45.
The common factors of 9 and 45 are 1, 3 and 9. But the greatest number of all these is 9.
Therefore, we get that the greatest common factor of 9 and 45 is 9.

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.