Question

Two sets of maths and science books containing 1680 and 1056 books respectively in a library have to be stacked in such a way that all the books are stored subject wise and the height of each stack is the same. Assuming that all the books are of the same thickness determine the total number of stacks.

Answer 1

hcf (each stack) = hcf (1680,1056) . = Find the prime factorization of 1056 1056 = 2 × 2 × 2 × 2 × 2 × 3 × 11 Find the prime factorization of 1680 1680 = 2 × 2 × 2 × 2 × 3 × 5 × 7 To find the gcf, multiply all the prime factors common to both numbers: Therefore, GCF = 2 × 2 × 2 × 2 × 3 GCF = 48 no of stacks of maths book = 1680/48 = 35 no of stacks of science book = 1056/48 =22 total stacks= 35+22=57