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FInd the number of odd divisors of 10!

 Dec 28, 2020
 #1
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+1

(1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 81, 105, 135, 175, 189, 225, 315, 405, 525, 567, 675, 945, 1575, 2025, 2835, 4725, 14175)>>Total==30 such numbers

 Dec 29, 2020
 #2
avatar+117576 
+1

 

10! =  10 * 9 * 8 * 7 * 6  * 5 * 4 * 3 * 2 * 1  =

 

(5 * 2) * (3 * 3) * ( 4 * 2)  * 7 * (3 * 2)  * 5 * (2 * 2)  * 3 * 2   =

 

(5 )  * (3^2)  * 7  * 3  * 5 * 3   = 

 

3^4  * 5^2  * 7^1 

 

The  number of odd divisors   = add 1  to each exponent ...take the product of these sums =   (4 + 1)(2 + 1) (1 + 1)  =  (5) (3) ( 2)   = 30 

 

(Just as the Guest said  !!! )

 

 

cool cool cool

 Dec 29, 2020
edited by CPhill  Dec 29, 2020
edited by CPhill  Dec 29, 2020

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