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  • A natural number has prime factorization given by , where y and z are such that y+z=5 and <img alt="y^{-1}+z^{-1}=\frac{5}{6}, y>z" sr

A natural number has prime factorization given by n = 2^x3^y5^z, where y and z are such that y+z=5 and y^{-1}+z^{-1}=\frac{5}{6}, y>z. Then the number of odd divisons of n, including 1, is:
Option: 1 6x
Option: 2 6
Option: 3 11
Option: 4 12

Answers (1)

best_answer

Given that

\\y+z=5 \\ \frac{1}{y}+\frac{1}{z}=\frac{5}{6} \\y>z\\\Rightarrow y=3,\;z=2

for calculating odd divisor of n = 2x3y5z

x must be zero

\\\Rightarrow \mathrm{n}=2^{\mathrm{0}} .3^{3} \cdot 5^{2}\\\therefore \text { total odd divisors must be }(3+1)(2+1)=12

Posted by

himanshu.meshram

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