Probability of divisibility ?

Number Theory Level 3

What is the Probability that a number N will be divisible by any number ?

1/(N-2) 1/N 1/(2) 1/(N-1)

Shivek Sood by Shivek Sood , 30, India

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1 solution

Shivek Sood
Dec 7, 2014

Every number is divisible by any other number if the remainder after division is 0 . A number N can have N remainders (0,1,2,3,4,5,6...........N-1) so to probability of a number being completely Divisible by a Number is 1/N

1 Helpful 0 Interesting 0 Brilliant 0 Confused

This is a fun question, Shivek, but the wording is open to interpretation. There is no "uniform" probability on the integers, so the probability in question is not well-defined. Also, once N N is (somehow) chosen, it will not be divisible by any numbers greater than itself, of which there will always be an infinite number. There is also the matter that any integer N N is divisible by 1 1 . So you might want to clarify what probability you are asking for.

This question is interesting because it leads to a discussion of the concept of natural density , so thank you for posting it. :)

Brian Charlesworth - 6 years, 6 months ago

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This was my first question i will try to make my wordings clear from next time. I will fix this soon Thanks

Shivek Sood - 6 years, 6 months ago

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