To find the shortest length that can be measured exactly by using each one of these rods, we need to find the LCM of their lengths.

$\begin{array}{cc}2& 6,4,8\\ 2& 3,2,4\\ 2& 3,1,2\\ 3& 3,1,1\\ & 1,1,1\end{array}$

LCM $=2\times 2\times 2\times 3=24cm$
Therefore, 24 cm is the shortest length that can be measured exactly by each one of these rods.

To get multiples of any number, we multiply counting numbers with that number.
Since there are infinite counting numbers, multiples of any number are also infinite.

Factors of 6: 1, 2, 3, 6
Factors of 4: 1, 2, 4
Common factors : 1 ,2
Hence, 6 and 4 have 2 common factors.

Factors of 13: 1, 13
Factors of 7: 1, 7
The only common factor is 1.
Hence the HCF of 13 and 17 is 1.

The largest factor of a number is the "number itself".
For example, the highest factor of 48 is 48.
The lowest factor of any number is 1.

1 is an unique number. It is neither a prime number nor a composite number. 
1 is the only number that does not have two factors.

Using the prime factorization method:

$\begin{array}{cc}2& 25,50,100\\ 5& 25,25,50\\ 5& 5,5,10\\ 2& 1,1,2\\ & 1,1,1\end{array}$
LCM of 25, 50 and 100 $=2\times 5\times 5\times 2=100$