Trailing zeros Problem!
The number of trailing zeros in 100! is
The answer is 24.
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3 solutions
A new way!
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And not confused, Swapnil bro, you should write " trailing zeroes", because your question could confuse everybody, leading all of us solvers to also find the number of 0's inside! :)
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oops, let me change it!
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@Swapnil Das – Also, no floor function is needed.
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@Bryan Lee Shi Yang – it is possible to calculate through it!
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@Swapnil Das – How? Maybe You can show us all, and teach us new things!
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@Bryan Lee Shi Yang – ⌊ 5 1 0 0 ⌋ + ⌊ 2 5 1 0 0 ⌋ = 2 0 + 4 = 2 4
@Bryan Lee Shi Yang – Greatest integer function with 5 as the divisors, its consecutive powers, try it out!
1 0 0 ! = 1 × 2 × 3 × . . . . . . . . . . . . . × 9 9 × 1 0 0 ,the no.of zeros in 100! = [ 5 1 1 0 0 ] + [ 5 2 1 0 0 ] . . . . . . . . . . . . . . . . . . Note:[2.3]=2 = > n o . o f . z e r o s = 2 0 + 4 + 0 + 0 + . . . . . . . . . . . . . . = 2 4
Given 1 0 0 ! = 2 x × 5 y × 3 z . . . . . . , there are 4 5 2 's and 16 5 1 's. (The number of 2's is not a problem.) So the number of TRAILING ZEROES, not ZEROES, is 4 × 2 + 1 6 = 2 4 .