Two sets of maths and science books contains 1680 and 1056 books respectively in a 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 . Assume that books are of the same thickness , determine the total number of stacks .

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Solution

No. of books in each stack = H.C.F of 1680 , 1056
Therefore ,
By using Euclid's lemma :
a = bq + r
$\Rightarrow 1680 = 1056.1 + 624$
$\Rightarrow 1056 = 624 \times 1 + 432$
$\Rightarrow 624 = 432 \times 1 + 192$
$\Rightarrow 432 = 192 \times 2 + 48$
$\Rightarrow 192 = 48 \times 2 + 0$
$∴$ Therefore HCF (1680 , 1056) = 48
So , there are 48 books in a stack.

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Two sets of maths and science books contains 1680 and 1056 books respectively in a 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 . Assume that books are of the same thickness , determine the total number of stacks .

No. of books in each stack = H.C.F of 1680 , 1056Therefore ,By using Euclid's lemma :a = bq + r⇒1680=1056.1+624⇒1056=624×1+432⇒624=432×1+192⇒432=192×2+48⇒192=48×2+0∴ Therefore HCF (1680 , 1056) = 48 So , there are 48 books in a stack.