At the time of tahajjud and fajr prayers, our hearts are most aware of the presence of Allah. The worldly affairs have not invaded our minds yet. There is no household work to do or job to go to, the only thing we have to do is worship God.
In the Quran Allah talks about those who will enter paradise. He (swt) tells us that this is easiest to attain in the last 10 nights of Ramadan and the first 10 days of Dhul Hijjah!