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k islargest positive integer such that 2009^k divides factorial 2010 exactly. find k

k islargest positive integer such that 2009^k divides factorial 2010 exactly. find k

Grade:12

3 Answers

jitender lakhanpal
62 Points
10 years ago

Dear manoj,

 there cant be any value of k for which 2009k can be divided by 2010

 

 

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manoj jain
14 Points
10 years ago

solution is not according to question

manoj jain
14 Points
10 years ago

2009 =7.7.41

2010! = 1.2.3............2010

        =   ( 7.14............82terms)(41.82............49terms) .others factors

        =    7^82(1.2.3............82)41^49(1.2.......49).other factors

        = 7^82  ( 7.14......11terms) (other factors )41^49(41)(other factors)  

         = 7^82.7^11.41^50.other factors     

         =( 7.7)^50.41 ^50 .otherfactors

        =(7.7.41)^50.other factors

         =(2009)50.other factrs

 k=50 ans 

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