Numerical answer
How many zeros are there at the end of 125! (125 factorial)?
Show answer and solution
Answer: 31
Trailing zeros come from factors of 10 = 2 × 5. There are far more 2s than 5s, so count the 5s.
⌊125/5⌋ = 25 (multiples of 5)
⌊125/25⌋ = 5 (multiples of 25 give an extra 5)
⌊125/125⌋ = 1 (125 = 5³ gives one more)
Total = 25 + 5 + 1 = 31.
Tip: Keep dividing by 5 and adding the quotients: 125 → 25 → 5 → 1, and 25 + 5 + 1 = 31.
⌊125/5⌋ = 25 (multiples of 5)
⌊125/25⌋ = 5 (multiples of 25 give an extra 5)
⌊125/125⌋ = 1 (125 = 5³ gives one more)
Total = 25 + 5 + 1 = 31.
Tip: Keep dividing by 5 and adding the quotients: 125 → 25 → 5 → 1, and 25 + 5 + 1 = 31.
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