# Successive Divisions

Algebra Level 3

A number $$N$$ when successively divided by $$3,5$$ and $$8$$ leaves remainders $$1,4$$ and $$7$$ respectively. The same number $$N$$ when successively divided by $$8, 5$$ and $$3$$ leaves remainder $$p, q$$ and $$r$$ respectively. Find $$100p+10q+r$$.

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