84. Three sets of Physics, Chemistry and Biology books have to be stacked in such a way that all the books are stored topic-wise and the height of each stack is the same. The number of Physics books is 105, the number of Chemistry books is 140 and the number of Biology books is 175. Assuming that the books are of the same thickness, determine the number of stacks of Physics, Chemistry and Biology books.

 In order to arrange the books as required, we have to find the largest number that divides 105, 140 and 175 exactly.

Clearly, required number is the HCF of 105, 140 and 175.

Case I :

I. Finding HCF of 105 and 140 by applying Euclid’s division lemma, we get



II. Since, the remainder 35 ≠ 0, we apply division lemma to get

Since, the remainder at this stage is zero, so the divisor i.e., 35 at this stage is the HCF of 105 and 140.

Case II :

I. Finding the HCF of 35 and 175 by applying Euclid’s division lemma, we get

II. Since the remainder at this stage is zero, so the divisor i.e., 35 at this stage is the HCF of 35 and 175.

Thus, HCF of 105, 140) and 175 is 35.

Now,

Number of stacks of Physics books



Number of stacks of Chemistry books





Number of stacks of Biology books