divide by 78 counter can be realized using

A divide by 78 counter can be realized using?

a) 6 number of mod 13 counters
b) 13 number of mod 6 counters
c) one mod-13 counter followed by one mod 6 counter
d) 13 number of mod-13 counters

The right answer is C. 78=13*6. The mod-13 counter will be incremented with each pulse of the incoming signal, and will overflow every 13 counts of such pulses. The mod-6 counter will be incremented each time that the mod-13 counter overflows. The mod-6 counter will overflow every 6 of its counts. Therefore, the mod-6 counter will overflow every 6*13=78 pulses of the incoming signal.

In other words, for each state of the mod-6 counter, the mod-13 counter counts 13 states. So, in total, you will have 6*13=78 different "global" states. That's why, if you have them one after the other (so that counter k increments one unit when counter k-1 overflows), you have to multiply the numbers of states, not add them.

These will be the count values for each of the two counters, before each pulse at the input.

Code:

{(mod-13 counter value) (mod-6 counter value)} 
{0 0} 
{1 0} 
... 
{12 0} 
{0 1} 
{1 1} 
... 
{12 1} 
{0 2} 
{1 2} 
... 
... 
{12 5} 
<-- Here is the overflow for the global counter formed. Above this line, there are 78 different states. 
{0 0} 
...