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Question
What is the remainder obtained when 100!+100 is divided by 101?
What is the remainder obtained when 100!+100 is divided by 101?
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Solution
The correct option is D 99
According to Wilson's theorem , if p is a prime number then (p-1)!+1 is divisible by p. So 100! can be written as 101k -1 , where k is an integer.
100!+100 = 101 k + 99.
So the remainder obtained is 99.
99
According to Wilson's theorem , if p is a prime number then (p-1)!+1 is divisible by p. So 100! can be written as 101k -1 , where k is an integer.
100!+100 = 101 k + 99.
So the remainder obtained is 99.
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