How many zeroes at end of 2005!
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Your question was
How many consecutive zeroes are there in 2005!
Answer: 401
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Step-by-step explanation :
To check how many 0's there, we have to find multiples below 2005.
We can observe 0 < multiples ≤ 2005
We can observe multiple of 2 is on the form 2k.
→ 0 < 2k ≤ 2005
→ 0 < k ≤ 1002.5
Therefore, there are 1002 multiples of 2.
In the same view, multiple of 5 is on the form 5k.
→ 0 < 5k ≤ 2005
→ 0 < k ≤ 401
Therefore, there are 401 multiples of 5.
We found that 2005! = (1002 multiples of 2) × (401 multiples of 5) × (other number)
Therefore 2005! is on the form 2¹⁰⁰² × 5⁴⁰¹ × k.
On simplifying, we know that 2005! is 10⁴⁰¹ × 2⁶⁰¹ × k
Therefore, there are 401 zeroes at the end.
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