“But I warn you – unless your righteousness is better than the righteousness of the teachers of religious law and the Pharisees, you will never enter the Kingdom of Heaven!”– Matthew 5:20 (NLT)

The teachers of the law and Pharisees made it their goal to be as righteous as humanly possible.  But the key word in that sentence is humanly.  Jesus demands that our righteous be better than theirs if we expect to enter the Kingdom of Heaven.  This is not humanly possible.  Happily, the Scriptures clear up this conundrum for us.  Paul explains it using the case of Abraham to illustrate:

Abraham was, humanly speaking, the founder of our Jewish nation. What were his experiences concerning this question of being saved by faith? Was it because of his good deeds that God accepted him? If so, he would have had something to boast about. But from God’s point of view Abraham had no basis at all for pride. For the Scriptures tell us, “Abraham believed God, so God declared him to be righteous.” – Romans 4:1-3 (NLT) 

He then takes that wonderful truth and applies it to us.  The best kind of righteousness is ours when we put our faith in Jesus. 

Now this wonderful truth-that God declared him to be righteous-wasn’t just for Abraham’s benefit. It was for us, too, assuring us that God will also declare us to be righteous if we believe in God, who brought Jesus our Lord back from the dead. He was handed over to die because of our sins, and he was raised from the dead to make us right with God. – Romans 4:23-25 (NLT)