240!

Number Theory Level 3

Find the number of consecutive zeroes at the end of 240!.

NOTE - 3000 have 3 zeroes. 301500 consist of two zeroes.
Consecutive zeroes at the end mean the number of 10s as factor.


The answer is 58.

Mayank Chaturvedi by Mayank Chaturvedi , 21, India

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3 solutions

Sunil Pradhan
Jul 10, 2014

divide 240 by 5 find quotient repeat the operations till quotient less than 5

add all quotients will give number of zeroes

240/5 = 48

48/5 = 9

9/5 = 1

48 + 9 + 1 = 58

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Bro make it box functions. It will be more clear.

Md Zuhair - 4 years, 8 months ago
Ryan Redz
Jun 4, 2014

240/5=48, 240/25 = 9.6 240/125 = 1.92. Add only the whole numbers quotient.... 48 + 9 + 1 = 58

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Perfect. That's the method to find number of 5s

Mayank Chaturvedi - 7 years ago
Mayank Chaturvedi
May 15, 2014

If we factories 240! , we get 5^58 as factor. As 5 and 2 are only the primes that produce zeroes, and obviously no. of fives are less, then no. of 2's , we get 58 zeroes

1 Helpful 0 Interesting 0 Brilliant 0 Confused

240/5=48 48/5=9 9/5=1 1/5=0

48+9+1 = 58.

Some of the numbers have more than 1 factor of 5.

brett bolen - 7 years ago

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