A natural number has prime Factorisation given by n=2x3y5z where y and Z are such that y+z=5 and y−1+z−1=56,y>z then the number of odd divisors of n including 1 is

n=2x3y5zNo of odd divisors of n=2x3352n=3+12+1=4×3=12y+z=5y−z2=y+z2−4yz=25−24y−z=1y+z=5 2y=6 y=3 z=2y−1+z−1=56y+zyz=565yz=56yz=6

A natural number has prime Factorisation given by n=2x3y5z where y and Z are such that y+z=5 and y−1+z−1=56,y>z then the number of odd divisors of n including 1 is

n=2x3y5zNo of odd divisors of n=2x3352n=3+12+1=4×3=12y+z=5y−z2=y+z2−4yz=25−24y−z=1y+z=5 2y=6 y=3 z=2y−1+z−1=56y+zyz=565yz=56yz=6

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A natural number has prime Factorisation 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

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Detailed Solution

$n = 2^{x} 3^{y} 5^{z}$

$No of odd divisors of n$

$= 2^{x} 3^{3} 5^{2}$

$= (3 + 1) (2 + 1)$

$= 4 \times 3 = 12$

$y + z = 5$

${(y - z)}^{2} = {(y + z)}^{2} - 4 y z$

$= 25 - 24$

$y - z = 1$

$y + z = 5 2 y = 6 y = 3 z = 2$

$y^{- 1} + z^{- 1} = \frac{5}{6}$

$\frac{y + z}{y z} = \frac{5}{6}$

$\frac{5}{y z} = \frac{5}{6}$

$y z = 6$

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A natural number has prime Factorisation given by n=2x3y5z where y and Z are such that y+z=5 and y−1+z−1=56,y>z then the number of odd divisors of n including 1 is

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A natural number has prime Factorisation 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