Question

What is the GCF of $40,60,80$

Answer 1

Hint: Here we have to find the Greatest Common Factor of the three numbers given. Firstly by using the long division method we will find the prime factors of all the three numbers given. Then we will take out the common factor from all three numbers. Finally we will multiply the common factors and get our desired answer.

Complete step by step answer:
We have to find the greatest common factor of the number given below:
$40,60,80$
Now we will find the prime factors of each number by using a long division method.
Firstly we will find the prime factor of $40$ by dividing it by first prime number that is $2$ and moving on to other prime number till we get the remainder as $1$ as follows:
$\begin{align}
  & 2\left| \!{\underline {\,
  40 \,}} \right. \\
 & 2\left| \!{\underline {\,
  20 \,}} \right. \\
 & 2\left| \!{\underline {\,
  10 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & \,\,\,1 \\
\end{align}$
So we got the factors as:
$40=2\times 2\times 2\times 5$……$\left( 1 \right)$
Next we will find the prime factor of $60$ by dividing it by first prime number that is $2$ and moving on to other prime number till we get the remainder as $1$ as follows:
$\begin{align}
  & 2\left| \!{\underline {\,
  60 \,}} \right. \\
 & 2\left| \!{\underline {\,
  30 \,}} \right. \\
 & 3\left| \!{\underline {\,
  15 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & \,\,\,1 \\
\end{align}$
So we got the factors as:
$60=2\times 2\times 3\times 5$….$\left( 2 \right)$
Next we will find the prime factor of $80$ by dividing it by first prime number that is $2$ and moving on to other prime number till we get the remainder as $1$ as follows:
$\begin{align}
  & 2\left| \!{\underline {\,
  80 \,}} \right. \\
 & 2\left| \!{\underline {\,
  40 \,}} \right. \\
 & 2\left| \!{\underline {\,
  20 \,}} \right. \\
 & 2\left| \!{\underline {\,
  10 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & \,\,\,1 \\
\end{align}$
So we got the factors as:
$80=2\times 2\times 2\times 2\times 5$….$\left( 2 \right)$
On comparing equation (1) (2) and (3) we get the common factors as follows:
$\Rightarrow 2\times 2\times 5$
$\Rightarrow 20$
So we got the answer as $20$
Hence the Greatest Common Factor (GCF) of $40,60,80$ is $20$ .

Note: Greatest Common factor is the greatest number that can divide all the given numbers or we can say that which is the factor of all the three numbers. We have used the prime factorization method as it becomes easy to get the common factors by having the factors in prime numbers. Factors are the number which when multiplied gives back the number.