Trailing 0's
Number Theory
Level
3
Which of the following can be the number of trailing zeros in , where is a natural number ?
91
89
73
85
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1 solution
The number of trailing zeroes in 3 6 5 ! is
⌊ 5 3 6 5 ⌋ + ⌊ 2 5 3 6 5 ⌋ + ⌊ 1 2 5 3 6 5 ⌋ = 7 3 + 1 4 + 2 = 8 9 .