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Last three digits (Posted on 2011-10-19) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
two-thirds of a solution. | Comment 1 of 9
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

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