Question

How do you find the GCF of $20,21$ and $25$?

Answer 1

Hint: We will find the factors of all the three given numbers one by one and then select the greatest factor which is common to all the three given numbers. Finally we conclude the required answer.

Complete step-by-step solution:
The given numbers are: $20,21$ and $25$.
Now to find the greatest common factor we will find the factors of the numbers.
The factors of $20$ are all the numbers between $1$ and $20$ which divide $20$ evenly which means without any remainder.
The numbers are: $1,2,4,5,10,20$, all these numbers divide $20$ without leaving any remainder.
Now, we find out the second value,
The factors of $21$ are all the numbers between $1$ and $21$ which divide $21$ evenly which means without any remainder. The numbers are:
$1,3,7,21$, all these numbers divide $21$ without leaving any remainder.
Now, we find the last value,
The factors of $25$ are all the numbers between $1$ and $25$ which divide $25$ evenly which means without any remainder. The numbers are:
$1,5,25$, all these numbers divide $25$ without leaving any remainder.
Now writing the factors for all the numbers together we get:
$20:1,2,4,5,10,20$
$21:1,3,7,21$
$25:1,5,25$
Now the factor which is common to all the numbers is $1$.
Since there is no other factor which is greater than $1$, the GCF is $1$.

Therefore, the GCF of $20,21$ and $25$ is $1$, which is the required answer.

Note: The greatest common factor of numbers is used for simplification purposes in an equation.
It is to be remembered that for a number, $1$ and the number itself will be the factors of that number.
There also exists the LCM which stands for the lowest common multiple which is the lowest multiple which two or more numbers have in common. The LCM is used to simplify fractions.