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Factorial Remainder (Posted on 2011-09-02)

Determine the remainder when 98! is divided by 101

*** For an extra challenge, solve this problem without using a computer program.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Trying to avoid 98 mods...

| Comment 2 of 9 |

98! ends with 22 zeroes. What is the remainder when 10^22 us divided by 101?

1/101 = 99/9999 = .009900990099...
so 10^22/101=99009900990099009900.9900990099..
that decimal representing 100/101

Im not sure how to save much work from here but you could now leave out a total of 22 twos and all the fives as factors in doing what Joshua did.

Posted by Jer on 2011-09-02 14:56:06

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