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Cleanliness may refer to physical and mental and behavioural. 

Cleanliness is a good habit and very useful for all of us. When we keep ourselves clean physically we are not allowing any bad insects or diseases or germs to grow. We are not allowing bad things to flourish. Our physique stays healthy. We will be able to think of good thoughts.

When we keep the surroundings clean, we are not allowing the demon-like germs, insects and diseases to spread around the world and cause damage to neighbouring people. We are directly or indirectly helping others.  We are also teaching good habits to ignorant people.

When we see clean things and pure things around, we do not get bad ideas. We feel happy in heart and mind and we will be inclined to help others. So we are healthy mentally and in heart.  We do not think too selfishly to exploit or cheat others for their own benefit.  

We can not do what all God can do.  God helps all persons.  But we can do next to being Godly, as we help others to be in good health and to be good.  Children and saints (sages) are said to be Gods or God's people.  Because they keep their minds clean. They do not pollute the environment. The clean people think of good things for the mankind.  They cure the bad qualities of the bad people.  They obey the laws of nature.  They try for the good of human kind. This is what God wants.

People with clean minds are good, helpful.  They work for prosperity of all humanity and animals too.  They help others and protect others like God does.

So cleanliness is next to Godliness.