BMO 1965 Problem 4 What is the largest power of 10 dividing 100 x 99 x 98 x ... x 1? Solution
: 24. There are 20 multiples of 5: 1·5, 2·5, ... , 20·5. Of these 4 are multiples of 25: 1·25, 2·25, 3·25, 4·25. None are multiples of 125. Hence the highest power of 5 dividing 100! is 24. The highest power of 2 is obviously higher. 1st BMO 1965 © John Scholes jscholes@kalva.demon.co.uk 30 Aug 2000