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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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