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A librarian wants to arrange 154 english books and 84 mathematics books in shelves such that each shelf contains the same number of books. Also each shelf should contain either only English books or only mathematics books . She wants to arrange them in such a way that the least number of shelves is used . What will be the number of books in each shelf

We have,number of English books = 154number of Maths books = 84Let us find the HCF of 154 and 84.The prime factorisation of 154 and 84 are :154 = 2×7×1184 = 2 × 2 × 3 × 7HCF of 154 and 84 = 2×7 = 14Hence, each shelf has to contain 14 books so that number of shelves used may be least.

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no. of  english books=154
no. of  maths books=84
no. of books in each shelf=?
hence we need to find it's HCF
154=84*1+70
84=70*1+14
70=14*5+1
hence the no. of  books in each shelf without mixing subjects and using least no. of shelves is 14





 
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Take the H.C.F
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HCF is 14      
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