Question Number 34369 by Rasheed.Sindhi last updated on 05/May/18
$$\mathrm{Determine}\:\mathrm{number}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{pairs},\mathrm{whose} \\ $$$$\mathrm{GCD}\:\mathrm{is}\:\mathrm{144}\:\mathrm{in}\:\mathrm{case}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{when}\:\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{and}\:\left(\mathrm{b},\mathrm{a}\right)\:\mathrm{is}\:\mathrm{considerd} \\ $$$$\:\:\:\:\:\:\:\mathrm{same}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{when}\:\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{and}\:\left(\mathrm{b},\mathrm{a}\right)\:\mathrm{is}\:\mathrm{considerd} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{different}. \\ $$
Answered by MJS last updated on 05/May/18
$${a}=\mathrm{144}×\Pi{p}_{{i}} \\ $$$${b}=\mathrm{144}×\Pi{p}_{{j}} \\ $$$${p}_{{i}} \neq{p}_{{j}} \:\forall\left({i};{j}\right) \\ $$$$\left(\mathrm{i}\right),\:\left(\mathrm{ii}\right)\:\mathrm{answer}\:\mathrm{is}\:\infty \\ $$
Commented by Rasheed.Sindhi last updated on 05/May/18
$$\mathrm{Than}\mathcal{X}\:\mathrm{a}\:\mathrm{lot}\:\boldsymbol{\mathrm{sir}}! \\ $$