N is the product of all the prime numbers less than 100.

Determine the last three digits of N.

*** For an extra challenge, solve this puzzle without the aid of a computer program.

2   3   5   7  11  13  17  19  23  29 
31  37  41  43 47  53  59  61  67  71   73  79  83  89  97 

Clearly the 2 and 5 make the last digit 10.  Of the others,
five end in 1,  seven end in 3, six end in 7, five end in 9.

3^7 = 2187
7^6 ends in 9
9^5 ends in 9

7*9*9 ends in 7

So the last TWO digits of N are 70.

That third digit from the end looks quite a bit more complicated, at least without a computation aid.

Edited on October 19, 2011, 11:10 am

Posted by Jer on 2011-10-19 11:08:01