Number of natural solutions of the equation x | vedclass

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Question

$xyz = {2^5} 	imes {3^2} 	imes {5^2}$

let   $x = {2^{{a_1}}}{3^{{b_1}}}{5^{{c_1}}}$

$y = {2^{{a_2}}}{3^{{b_2}}}{5^{{c_2}}}$

$z =

Vedclass · Accepted Answer

$756$

Vedclass · Answer

$xyz = {2^5} 	imes {3^2} 	imes {5^2}$

let   $x = {2^{{a_1}}}{3^{{b_1}}}{5^{{c_1}}}$

$y = {2^{{a_2}}}{3^{{b_2}}}{5^{{c_2}}}$

$z = {2^{{a_3}}}{3^{{b_3}}}{5^{{c_3}}}$

then  $xyz = {2^{{a_1} + {a_2} + {a_3}}}{3^{{b_1} + {b_2} + {b_3}}}{5^{{c_1} + {c_2} + {c_3}}}$

$ \Rightarrow {a_1} + {a_1} + {a_1} = 5$

${b_2} + {b_2} + {b_3} = 2$

${c_1} + {c_2} + {c_3} = 2$

Number of natural solutions of the equation $xyz = 2^5 \times 3^2 \times 5^2$ is equal to

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