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Question Number 34369 by Rasheed.Sindhi last updated on 05/May/18

Determine number of possible pairs,whose  GCD is 144 in case:  (i) when (a,b) and (b,a) is considerd         same.  (ii) when (a,b) and (b,a) is considerd           different.

$$\mathrm{Determine}\:\mathrm{number}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{pairs},\mathrm{whose} \\ $$$$\mathrm{GCD}\:\mathrm{is}\:\mathrm{144}\:\mathrm{in}\:\mathrm{case}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{when}\:\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{and}\:\left(\mathrm{b},\mathrm{a}\right)\:\mathrm{is}\:\mathrm{considerd} \\ $$$$\:\:\:\:\:\:\:\mathrm{same}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{when}\:\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{and}\:\left(\mathrm{b},\mathrm{a}\right)\:\mathrm{is}\:\mathrm{considerd} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{different}. \\ $$

Answered by MJS last updated on 05/May/18

a=144×Πp_i   b=144×Πp_j   p_i ≠p_j  ∀(i;j)  (i), (ii) answer is ∞

$${a}=\mathrm{144}×\Pi{p}_{{i}} \\ $$$${b}=\mathrm{144}×\Pi{p}_{{j}} \\ $$$${p}_{{i}} \neq{p}_{{j}} \:\forall\left({i};{j}\right) \\ $$$$\left(\mathrm{i}\right),\:\left(\mathrm{ii}\right)\:\mathrm{answer}\:\mathrm{is}\:\infty \\ $$

Commented by Rasheed.Sindhi last updated on 05/May/18

ThanX a lot sir!

$$\mathrm{Than}\mathcal{X}\:\mathrm{a}\:\mathrm{lot}\:\boldsymbol{\mathrm{sir}}! \\ $$

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