# Multiples of 864

If a positive integer multiple of 864 is chosen randomly, with each multiple having the same probability of being chosen, what is the probability that it is divisible by 1944?

- 5 August, 2012 -
- Article, Math Problems -
- Tags : 104 problems, number theory, titu
- 0 Comments

This can be easily solve by dividing out the greatest common divisor between 864 and 1944.

(1)

Since and , this problem becomes equivalent to the one of finding the probability of randomly chosen positive integer multiples of is divisible by . Since and are coprime, we only can be considered. Hence, that probability is .