(49g 50g) Number of Trailing Zeros in N!

[John Keith]

Inspired by this program and others by member GeraldH, this program will return A027868(n), the number of trailing zeros in n!.

Using ListExt 1.3, it is reasonably small and very fast, even for numbers with over 100 digits. The program is based on the third comment in the OEIS link above.

Code:


\<< DUP I\->R 5. \>=        @ Check that n >= 5
    { 5 I\->BL REV TAIL     @ Base 5 digits of n
      1 5 PICK3 SIZE LMSEQ  @ List of powers of 5
      :: + LSCAN            @ A003463
      * LSUM }              @ Sum of products
    { DROP 0 } IFTE         @ Return 0 for n<5
\>>