Question

What is the GCF of $27$ and $45$?

Answer 1

Hint: The full form of the GCF is the greatest common factor. The greatest common factor is a greatest number that is a factor of two or more other numbers. Or we can say when we find all the factors of two or more numbers, and some factors are the same or common, then the largest of those common factors is the greatest common factor. The greatest common factor is also known as the highest common factor. Now, what is the meaning of factor? A factor is a number that divides the number evenly into the original number, or we can say that the remainder becomes zero when we divide any number with their factor.

Complete step by step solution:
The given numbers which we have to find the GCF are $27$ and $45$.
To find the GCF of any numbers the procedure is:
1 First we write all the factors of each number.
2 And then from these numbers we choose the common factor.
3 And from the common factor we marked the greatest factor, and that greatest factor is GCF.
Now the factors of both the given numbers are:
$\begin{align}
  & \Rightarrow 27=\left\{ 1,3,9,27 \right\} \\
 & \Rightarrow 45=\left\{ 1,3,5,9,15,45 \right\} \\
\end{align}$
Now make a list of common factors, which are:
$\Rightarrow \left( 27,45 \right)=\left\{ 1,3,9 \right\}$
Now we can easily see that the greatest in these common factors is $9$.

Hence we get the common factor of $27$ and $45$ is $9$.

Note: We can also calculate the GCF of any number by using the prime factorization method. We know in prime factorization we write the given number in the form of multiplication of prime numbers.
So, the prime factorization of $27$ will be $=3\times 9$
And the prime factorization of $45$ will be $=9\times 5$
So here we can see the greatest common factor is $9$. Hence we get the same answer as we solved above.