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# A very difficult maths factorial problem? watch

1. 10! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10
10! = 1 x 2 x 3 x 4 . . . x 10

Write down the last 3 digits of this number. (Not 4 x ... but 4...)
2. 800
3. i think its 400
4. Tis 800...
5. 10!=3628800
6. guessing you want to do this without actually doing any long multiplication

10!
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10
= 1 x 3 x 4 x 6 x 7 x 8 x 9 x (2x5) x 10
= 1 x 3 x 4 x 6 x 7 x 8 x 9 x 100 [last 2 digits are 0]

then

1 * 3 mod 10 = 3
3 * 4 mod 10 = 2
2 * 6 mod 10 = 2
2 * 7 mod 10 = 4
4 * 8 mod 10 = 2
2 * 9 mod 10 = 8 [3rd from last digit is 8]
so the last 3 digits are 800
7. thanks

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Updated: January 28, 2010
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