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Question Number 27922 by Rasheed.Sindhi last updated on 17/Jan/18

$$\mathrm{a},\mathrm{b}\mathrm{\&}\mathrm{c}\mathrm{are}\mathbf{distinct}\mathbf{primes}\mathrm{and}$$$$\mathrm{x},\mathrm{y},\mathrm{z}\in \{0,1,2,\dots \}.$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathbf{divisors},$$$$\mathbf{common}\mathrm{to}\mathrm{the}\mathbf{numbers}{\mathbf{a}}^{\mathbf{x}}{\mathbf{b}}^{\mathbf{y}}{\mathbf{c}}^{\mathbf{z}},$$$${\mathbf{a}}^{\mathbf{x}}{\mathbf{b}}^{\mathbf{z}}{\mathbf{c}}^{\mathbf{y}},{\mathbf{a}}^{\mathbf{y}}{\mathbf{b}}^{\mathbf{x}}{\mathbf{c}}^{\mathbf{z}},{\mathbf{a}}^{\mathbf{y}}{\mathbf{b}}^{\mathbf{z}}{\mathbf{c}}^{\mathbf{x}},{\mathbf{a}}^{\mathbf{z}}{\mathbf{b}}^{\mathbf{x}}{\mathbf{c}}^{\mathbf{y}}\mathrm{\&}{\mathbf{a}}^{\mathbf{z}}{\mathbf{b}}^{\mathbf{y}}{\mathbf{c}}^{\mathbf{z}}.$$

Commented by mrW2 last updated on 17/Jan/18

$$AccordingtoQ27888,itis{[1+min(x,y,z)]}^3.$$

Commented by Rasheed.Sindhi last updated on 17/Jan/18

$$\mathrm{Yes}\mathrm{sir}\mathrm{I}\mathrm{thought}\mathrm{so}\mathrm{and}\mathrm{can}\mathrm{be}$$$$\mathrm{extended}\mathrm{to}{[1+\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})]}^{\mathrm{n}}$$$$\mathrm{Common}\mathrm{divisors}:$$$${\mathrm{a}}_1^{0,1,..,\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})}{\mathrm{a}}_2^{0,1,..,\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})}\dots {\mathrm{a}}_{\mathrm{n}}^{0,1,..,\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})}$$$$\mathrm{Number}\mathrm{of}\mathrm{common}\mathrm{divisors}=$$$${[1+\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})]}^{\mathrm{n}}$$

Commented by mrW2 last updated on 17/Jan/18

$${That}^{\prime }sabsolutelycorrectsir.$$$$Ithinkyoumeantinlastline$$$${[1+\min ({\mathrm{x}}_1,{\mathrm{x}}_2,..,{\mathrm{x}}_{\mathrm{n}})]}^{\mathrm{n}}$$

Commented by Rasheed.Sindhi last updated on 17/Jan/18

$$\mathrm{Yes}\mathrm{Sir}\mathrm{commit}\mathrm{mistake}\mathrm{mistakenly}.$$

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