$30!$

Number Theory Level 3

$30!$ ends in $7$ zeroes. What is the digit preceding those zeroes?

1 solution

Sahil Gohan
Jul 12, 2014

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

  1,  2,  3,  4,  5,  6,  7,  8,  9,  20

  1,  2,  3,  4,  5,  6,  7,  8,  9,  30

now we will get 3 zeros from 10, 20, 30 and 4 zeros by multiplying 5, 15, 25 with 2, 2, 4 respectively.

after that we get..now multiply just the units digit in each successive multiplication

   1,  2,  3,  1,  1,  6,  7,  8,  9,  1 = 4

   1,  2,  3,  1,  3,  6,  7,  8,  9,  2 = 4

   1,  2,  3,  4,  1,  6,  7,  8,  9,  3 = 8

now 4 4 =6 => 6 8 = 8

units multiplication :3 i like this one

Mu'amar Musa Nurwigantara - 6 years, 11 months ago

Is there any more energy efficient way to do this..? :P

Prateek Singhal - 6 years, 10 months ago

NO. This is the best option. :D

Aayush Todi - 6 years, 10 months ago