The number of ordered triplets $(x, y, z)$ where $x, y$ and $z$ are positive integers which satisfy the equation $x y z = 24$ is

24

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20

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24

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30

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Solution

The correct option is D $30$
$x y z = 24$
Prime factorisation,
$24 = 2^{3} \times 3^{1}$
$\Rightarrow x y z = 2^{3} \times 3^{1}$
No. of the division are $(3_{C_{1}} + {2.3}_{C_{2}} + 3_{C_{3}}) (3_{C_{1}}) = (3 + 6 + 1) (3) = 30$

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