Problem 7.

The symbol n! is read "n factorial" and means the product of the first n positive integers: 1 · 2 · . . . · (n - 2) · (n - 1) · n. Let p be the positive integer which is the largest power of 3 which divides evenly into 100! (100 factorial). That is, divides into 100! leaving no remainder, but has a remainder when it is divided into 100! Find p.

[Problem submitted by Don Hentschel, LACC Assistant Professor of Mathematics.]