jee-main 2021 Q61

jee-main · India · session1_26feb_shift2 Number Theory Divisibility and Divisor Analysis

A natural number has prime factorization given by $n = 2 ^ { x } 3 ^ { y } 5 ^ { z }$, 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 divisors of $n$, including 1 , is:
(1) 12
(2) 6
(3) 11
(4) $6 x$

A natural number has prime factorization given by $n = 2 ^ { x } 3 ^ { y } 5 ^ { z }$, 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 divisors of $n$, including 1 , is:\\
(1) 12\\
(2) 6\\
(3) 11\\
(4) $6 x$

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