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 20111019 11:08:01 