Question

Find the common factors of $5,15,25$

Answer 1

Hint: Here we are given three numbers $5,15,25$ and we need to find the common factors of these three numbers. So first of all, we need to find the individual factors of these three numbers. After that we can see the factors that are common in all of them.

Complete step-by-step answer:
Let us firstly find the factor of $5$
We can write $5$ as:
$
  5 = 1 \times 5 \\
  5 = 5 \times 1 \\
 $
So we can see that it has only two factors $1{\text{ and 5}}$$ - - - (1)$
Now we need to see the factors of $15$
We can write $15$ as:
$
  15 = 1 \times 15 \\
  15 = 3 \times 5 \\
  15 = 5 \times 3 \\
  15 = 15 \times 1 \\
 $
So we can say that the factors of $15$ are $1,3,5,15$$ - - - (2)$
Now we can write the factors of $25$
We can write $25$ as:
$
  25 = 1 \times 25 \\
  25 = 5 \times 5 \\
  25 = 25 \times 1 \\
 $
So we can say that the factors of $25$are $1,5,25$$ - - - - (3)$
So we finally get all the factors of $5,15,25$
We can see factors of $5 = 1,5$
Factors of $15 = 1,3,5,15$
Factors of $25 = 1,5,25$
Now we can notice from above three equations that $1$ is the factor that is present in all the numbers $5,15,25$
So we can say that it is one of the common factors of the number $5,15,25$
Similarly we can see that $5$ is also the factor present in all the numbers. Hence it is also the common factor of all of them.
But if we see $3,15,25$ they are not the factor common to all the numbers $5,15,25$
Hence we can say that common factors of $5,15,25$ are $1,5$.

Note: Here we must take care that $1$ is also to be taken into account while taking the common factor because it is the factor of every number. If we are given two different prime numbers then their common factor will only be $1$