Question

What is the GCF of 18 and 30?

Answer 1

Hint: To solve this question, we should know what $GCF$ is $GCF$ or Greatest Common Factor of two or more numbers is a factor or we can say the highest factor that is common in all those numbers. This can be done by writing all the factors in the smallest form and then multiplying all the common factors found among them.

Complete step-by-step solution:
Here, in this question, we have been asked to find the $GCF$ of 18 and 30. So, for doing that, we have to first find the factors of both 18 and 30. So, let us find the factors of 30 first. So, we have the factors of 30 as,
$\begin{align}
  & 2\left| \!{\underline {\,
  30 \,}} \right. \\
 & 3\left| \!{\underline {\,
  15 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & 1 \\
\end{align}$
Therefore, $30=2\times 3\times 5$.
So, we get that 2, 3 and 5 are all the factors of 30.
Similarly, we will find the factors of 18. So, we have the factors of 18 as follows,
$\begin{align}
  & 2\left| \!{\underline {\,
  18 \,}} \right. \\
 & 3\left| \!{\underline {\,
  9 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & 1 \\
\end{align}$
Therefore, $18=2\times 3\times 3$
So, we get the factors of 18 as 2, 3 and 3.
Now, when we consider the factors of 18 and 30, we can see that both have 2 and 3 as the common factors. And so, the $GCF$ will be the product of 2 and 3. So, we get the $GCF$ as,
$\begin{align}
  & GCF=2\times 3 \\
 & \Rightarrow GCF=6 \\
\end{align}$
So, we get the $GCF$ of 18 and 30 as 6.

Note: We can also find the $GCF$ using another method, that is the successive division. If we have a, b as the numbers, then we take the smaller number and divide the bigger number by it. And then we divide the divisor by the remainder. We will keep doing this until the remainder becomes zero and the last divisor is the $GCF$. This works great with bigger numbers.