Mathematics Question(quickly)

Find the units digit of the expression 1x2x3x...x2009x2010.

briefly explain your answer.

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  • 1 十年前
    最愛解答

    Method 1 ,1x2x3x...x2009x2010= (1 x 2 x 3 x 4 x 5) x 6 x 7 x 8 x ... x 2009 x 2010= (10 x 1 x 3 x 4) x 6 x 7 x 8 x ... x 2009 x 2010 which is a multiple of 10 ,so the units digit of the expression is 0.

    Method 2 ,1x2x3x...x2009x2010= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x (10) x 11 x 12 x ... x 2009 x 2010= 10 x (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9) x 11 x 12 x ... x 2009 x 2010which is a multiple of 10 , so the units digit of the expression is 0.

    Method 3 ,Since the units digit of 2010 is 0 , so the units digit of the expression is 0 also.

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