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 = …, y > z. Then the number of odd divisions of n, including 1, is :

Option C. y + z = 5 ....... (1)

Permutations and Combinations

JEE Main 2021 · 26 Feb, Evening shift · Q4805

MathematicsMedium98×since 2002Q4805

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 =

{5 \over 6}

, y > z. Then the number of odd divisions of n, including 1, is :

JEE Main 2021 · 26 Feb, Evening shift · Q4805

MathematicsMedium98×since 2002Q4805

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 =

{5 \over 6}

, y > z. Then the number of odd divisions of n, including 1, is :