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16! divided by 19.what is the answer?plz explain the process by wilson method.

16! divided by 19.what is the answer?plz explain the process by wilson method.

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http://www.pagalguy.com/forums/quantitative-ability-and-di/number-system-questions-and-discussions-t-43728

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according to wilsons th (n-1)!+1 is divisible by n. So (18!+1) is divisible by 19.

18!+1=19k ->18*17*16! +1=19k -->(19-1)*(19-2)*16! +1=19k

-->(19)^2 *16! - 3*19*16! +2*16! + 1=19k. Now the first two terms are obviously divisible by 19.So we will look at the last two terms only to get the remainder.

2*16! + 1=19k-->2*16!=19k -1 -->19m + 18(Since we are only interested in finding remainder we will express -1 in another equivalent way so that we get a multiple of 2)

--> 16!=19m/2 + 9 -->16!=19n + 9(m has to be a multiple of 2 since factorial cannot be a fraction)

hence on dividing 16! by 19 we get remainder of 9.

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16! divided by 19.what is the answer?plz explain the process by wilson method.

Commenting on this post has been disabled by the moderator.