Question
Download Solution PDFFind the number of consecutive zeroes at the end of 572!.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Find the number of consecutive zeroes at the end of 572!.
Formula used:
The number of trailing zeroes in n! is given by:
Trailing Zeroes = ⌊n/5⌋ + ⌊n/52⌋ + ⌊n/53⌋ + ...
Continue until ⌊n/5k⌋ = 0.
Calculation:
n = 572
⇒ Trailing Zeroes = ⌊572/5⌋ + ⌊572/25⌋ + ⌊572/125⌋ + ⌊572/625⌋
⇒ Trailing Zeroes = ⌊114.4⌋ + ⌊22.88⌋ + ⌊4.576⌋ + ⌊0.9152⌋
⇒ Trailing Zeroes = 114 + 22 + 4 + 0
⇒ Trailing Zeroes = 140
∴ The correct answer is option (1).
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