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    The digit of hundred's place value of 19! is:
    Question

    The digit of hundred's place value of 19! is:

    A.

    1

    B.

    4

    C.

    9

    D.

    0

    Correct option is D

    Given:

    Find the hundreds digit of ( 19! )

    Solution:

    19! = 19×18×17××1 \times 18 \times 17 \times \ldots \times 1​​

    ( 19!) is divisible by ( 1000) (since ( 10!) already has more than three factors of 2 and 5).

    Therefore, (19!mod 1000=0)( 19! \mod 1000 = 0 )​​

    ( 000).

    Thus, the hundreds digit is ( 0) 

    Alternate Method: 

    19! 

    If the last digit is 5, it becomes 0 when multiplied by 2 

    15, 5 ,10 

    So that 000 

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