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Determine the largest positive integer N such that 2022! is divisible by 10^N.

 Aug 23, 2022
 #1
avatar+124596 
+3

Divide 2022  by successive positive integer powers of 5 until 2022/ 5^n  produces a division < 1

 

integer [ 2022 / 5^1] =  404

integer [ 2022/ 5^2 ] = 80

integer [ 2022/ 5^3 ] = 16

integer [2022/ 5^4 ]  = 3

integer [ 2022 / 5^5 ]  = 0

 

N =  404 + 80 +16 + 3   =  503   CORRECTED  !!!!

 

 

cool cool cool

 Aug 23, 2022
edited by CPhill  Aug 23, 2022
edited by CPhill  Aug 23, 2022
 #2
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+2

wouldnt 2022/5^2 be 80 not 88?

Guest Aug 23, 2022
 #3
avatar+124596 
+2

 

 

Thx for pointing out my mistake....now  corrected  !!!

 

 

cool cool cool

CPhill  Aug 23, 2022
edited by CPhill  Aug 23, 2022
 #4
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0

thank you!

Guest Aug 23, 2022

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