14. There is a neat trick you can use with any factorial to know the number of zeroes at the end. All the zeros come from multiples of 10=2*5. There are a lot of 2s in the prime factors of 60!, so you only need to find all the multiples of 5 because you'll have as many zeroes at the end as factors of 5. To find the factors that are multiples of 5 just keep dividing by 5 until you get to a number below 1, discard all the decimals and add all the integers, like so: 60/5 = 12 (the 12 factors are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60) 12/5 = 2.4 (the next 2 factors are: 25 and 50. Yes they count twice because they have 2 fives as factors: 25=5*5, 50=5*5*2) Answer 12+2 = 14. There are 14 zeroes at the end of 60!. By the way, if you google for it you will find the number, and it does indeed have 14 zeroes at the end! :-) Not all problems requires a program. Happy coding! Z
________________________________ From: java-ee-j2ee-programming-with-passion@googlegroups.com [mailto:java-ee-j2ee-programming-with-pass...@googlegroups.com] On Behalf Of ANUJ KUMAR Sent: sábado, 18 de Julho de 2009 22:01 To: java-ee-j2ee-programming-with-passion@googlegroups.com Subject: [java ee programming] how many zero's are there at the end of 60 factorial --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Java EE (J2EE) Programming with Passion!" group. To post to this group, send email to java-ee-j2ee-programming-with-passion@googlegroups.com To unsubscribe from this group, send email to java-ee-j2ee-programming-with-passion-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/java-ee-j2ee-programming-with-passion?hl=en?hl=en -~----------~----~----~----~------~----~------~--~---
