Let y be an element of the set A $$=$$ $${1$$, $$2$$, $$3$$, $$5$$, $$6$$, $$10$$, $$15$$, $$30}$$ and $$x1$$, $$x2$$, $$x3$$ be integers such that $$x1x2x3$$ $$=$$ y, then the number of positive integral solutions of $$x1x2x3$$ $$=$$ y is

Question

Let y be an element of the set A $$=$$ $${1$$, $$2$$, $$3$$, $$5$$, $$6$$, $$10$$, $$15$$, $$30}$$ and $$x1$$, $$x2$$, $$x3$$ be integers such that $$x1x2x3$$ $$=$$ y, then the number of positive integral solutions of $$x1x2x3$$ $$=$$ y is

Infinity Learn · Accepted Answer

Number of solutions of the given equation is the same as the number of solutions of the $$equationx1x2x3x4=30=2$$×$$3$$×$$5Here$$, $$x4$$ is there because if $$x1x2x3$$ $$=$$ $$15$$, then $$x4$$ $$=$$ $$2$$ and if $$x1x2x3$$ $$=$$ $$5$$, then $$x4$$ $$=$$ $$6$$, etc.$$x4$$ is in fact a dummy variable.Each of $$2$$, $$3$$ and $$5$$ will be a factor of exactly one of $$x1$$, $$x2$$, $$x3$$, $$x4$$ in $$4$$ ways.∴ Required number $$=$$ $$43$$ $$=$$ $$64$$

Let y be an element of the set A = {1, 2, 3, 5, 6, 10, 15, 30} and x₁, x₂, x₃ be integers such that x₁x₂x₃ = y, then the number of positive integral solutions of x₁x₂x₃ = y is

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Let y be an element of the set A = {1, 2, 3, 5, 6, 10, 15, 30} and x1, x2, x3 be integers such that x1x2x3 = y, then the number of positive integral solutions of x1x2x3 = y is

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Let y be an element of the set A = {1, 2, 3, 5, 6, 10, 15, 30} and x₁, x₂, x₃ be integers such that x₁x₂x₃ = y, then the number of positive integral solutions of x₁x₂x₃ = y is