Question

What is the greatest common factor of $4$ and $10$ ?

Answer 1

Hint: In this question, we have to find the greatest common factor of two numbers. Thus, we will use the least common multiple to get the solution. As we know, the greatest common factor is between two or more integers such that it is the largest positive integer that divides both the integers. So, we start solving this problem, by finding the LCM of both 4 and 10 individually, to get the factors of both the numbers. After that, we will see the common factors between them, to get the required greatest common factor of the same.

Complete step by step solution:
According to the problem, we have to find the value of greatest common factor of two numbers.
Thus, we will use the LCM method to get an accurate solution
The numbers given to us is $4$ and $10$ ---------- (1)
So, now we will first find the least common multiple of $4$ to get the factors for the same, we get
$\begin{align}
  & 2\left| \!{\underline {\,
 4 \,}} \right. \\
 & 2\left| \!{\underline {\,
 2 \,}} \right. \\
 & 1\left| \!{\underline {\,
 1 \,}} \right. \\
\end{align}$
Thus, the least common multiple of $4$ is equal to $2\times 2\times 1$ --------- (2)
Now, to get the factors we will find the least common multiple of $10$, we get
$\begin{align}
  & 2\left| \!{\underline {\,
 10 \,}} \right. \\
 & 5\left| \!{\underline {\,
 5 \,}} \right. \\
 & 1\left| \!{\underline {\,
 1 \,}} \right. \\
\end{align}$
Therefore, the LCM of $10$ is equal to $2\times 5\times 1$ ------------ (3)
So, for the greatest common factor, we have to find the common factor of $4$ and $10$ , thus from the value of equation (2) and (3), we get the GCD as $2$.
Therefore, the greatest common factor of $4$ and $10$ is equal to $2$.

Note: While solving this problem, do mention all the steps properly to avoid confusion and errors. Also, remember that greatest common factor and greatest common multiple means the same thing. Always take the highest common factor to find the greatest common factor.