Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

pythagoras123 Group Title

The product of n whole numbers 1 x 2 x 3 x 4 x ... x (n-1) x n, has twenty-eight consecutive zeros. Find the largest value of n.

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    what are zeros??

    • 2 years ago
  2. pythagoras123 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    "0". This is a zero. Consecutive zeros are zeros that appear consecutively, i.e. The product of 10 x 10x 10 has 3 consecutive zeros (1ooo)

    • 2 years ago
  3. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    It's somewhat tedious to explain the whole thing. One interesting observation is there would be only trailing zeroes.

    • 2 years ago
  4. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @ffm i'll try before you

    • 2 years ago
  5. pythagoras123 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Just tell me how you work it out, or the solution/methodology. The answer is not so important.

    • 2 years ago
  6. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i think between 1 and 10, you will have 2 zeros.

    • 2 years ago
  7. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I have used binary search along with the usual De Polignac's formula (just) twice to yield 124 as the answer. Ref: http://en.wikipedia.org/wiki/De_Polignac%27s_formula

    • 2 years ago
  8. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    "Consecutive zeros are zeros that appear consecutively, i.e. The product of 10 x 10x 10 has 3 consecutive zeros (1ooo)" You haven't understood the problem.

    • 2 years ago
  9. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry, 139

    • 2 years ago
  10. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @ffm is it correct??

    • 2 years ago
  11. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    33 for 139.

    • 2 years ago
  12. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I have posted the correct answer.

    • 2 years ago
  13. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ah ... where did i screwed up??

    • 2 years ago
  14. pythagoras123 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @FoolforMath, how did you manage to get 124?

    • 2 years ago
  15. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    looks like my theory screwed up from here http://www.wolframalpha.com/input/?i=30%21%2F20%21&dataset=&equal=Submit

    • 2 years ago
  16. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    3 zeros ,,,?? how 25*22 = 00 => two zeros were coming from here. so all the factors of 100 or 1000 or 10000 ... were causing problem for my idea.

    • 2 years ago
  17. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    1-10 : 2 zeros 10-20: 2 20-30: 3 (25 is factor of 100) 30-40: 2 40-50: 3 (50 is factor of 100) 60-60: 2 60-70: 2 70-80: 3 (at some point 75 will give two zeros) 80-90: 2 90-100: 3 (100 itself gives two) ----------------------- so from 0 to 100 we have: 24 zeros 100-110: 2 110-120: 2 ----------------------- I guess that would give 28 zeros screw you ---> minions of 100

    • 2 years ago
  18. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the answer was n = 120

    • 2 years ago
  19. Aron_West Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The largest power of 5 dividing n must be 5^28.Now use De Polignac's Formula.

    • 2 years ago
  20. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    120! = 6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000 Of course you need an analytic proof of that using 2 and 5.

    • 2 years ago
  21. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Should the question be, find the smallest n to achieve that?

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.