I found out that Mongol Empire had around 100,000 soldiers on the field. Most of them were cavalries and they had great battle tactics.
Isn't that figure however a bit low to conquer and control that huge land?
The mongols weren't fighting modem armies. 100k is huge for a medieval army. Most of what the mongols conquered were steppes which weren't very highly populated to start off with. The Chinese or Persians had large populations, but their infantry army was no match for mongol horse archers.
So basically the mongols were successful because 100k cavalry armies were very formidable.
The success of the mongolian army was built on more factors:
I think the success might have had more to do with tactics than with the size of the army on the field. One of the ingenious methods Genghis Khan employed to win over the loyalty of his enemies was the order to execute them (and their families) if they would not ally with him and his forces. The majority of the nomads was reported to have realigned allegiance in order to avoid the infamous brutal onslaught of the Mongol warriors. In return, those who switched camps were rewarded a peaceful life, and promised lands and food. As enemies throughout the steppes became allies, even though the area was huge, it was more efficient to win by politics than by sheer military conquests (although that was not uncommon towards those who were unwilling to change allegiance).
Fundamentally the major Mongol success was the conquest of China, and that was due to fact China was divided and Mongols were successful in getting large amounts of assistance by allying with Chinese factions.