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Non - Zero Digit (Posted on 2003-12-21) Difficulty: 4 of 5
What is the last non - zero digit in (20!)!? (That is, factorial of 20 factorial).

See The Solution Submitted by Ravi Raja    
Rating: 2.6667 (6 votes)

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re: simple solution | Comment 6 of 11 |
(In reply to simple solution by Tristan)

"making x!'s last nonzero digit repeat every 40"

The last non-zero digit does not repeat every 40.

Here are the last digits of the factorials of the first few multiples of 40:


40 2
80 8
120 6
160 6
200 2
240 6
280 4
320 4
360 6
400 8
440 2
480 6
520 6
560 4
600 6
640 8
680 4
720 6
760 4
800 6
840 6
880 6
920 8
960 6
1000 2
1040 4
1080 6
1120 2
1160 8
1200 6
1240 8
1280 6
1320 6
1360 4
1400 4
1440 6
1480 8
1520 4
1560 6
1600 4

--------
For the first couple,

40! = 815915283247897734345611269596115894272000000000
80! = 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000
  Posted by Charlie on 2003-12-22 08:43:51
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