Two sets of Math and Science books containing 1680 and 1056 books respectively in library have to be stacked in such a way that all the books are stored subjectwise and the height of each stack is the same. Assuming that the books are of the same thickness, determine the total number of stacks.
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The number of stacks of math books = 35
The number of stacks of science books = 22
Total stack of books = 57
Total number of maths books = 1680
Total number of science books = 1056
Total number of books in a stack is equal to the H.C.F of 1680 and 1056.
1680 = 2⁴ × 3 × 7 × 5
1056 = 2^5 × 11 × 3
H.C.F = 2⁴ × 3 = 48
Total stack of math books = 1680/48 = 35
Total stack of math books = 1056/48 = 22
Total stack of books = 57
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