The remainders when 4864 and 5800 are divided by a certain number, X, are the same. What is the maximum possible number of divisors of X?
In the explanation given - it says that X will be divisible by 5800-4864
Can someone explain how we can come up with this ?

Question

The remainders when 4864 and 5800 are divided by a certain number, X, are the same. What is the maximum possible number of divisors of X?
In the explanation given - it says that X will be divisible by 5800-4864
Can someone explain how we can come up with this ?

Varun Kumar Reddy · Answer

Hi Tanuj,Let us prove why X is a factor of the difference of the numberslet a,b,c be positive integers.4864 = aX+c5800 =bX+c(b-a)X = 936Maximum value X can have is 936 (i.e when (b-a) = 1).Hence we calculate the divisors for 936.Hope that helps.Thanks,Varun.

The remainders when 4864 and 5800 are divided by a certain number, X, are the same. What is the maximum possible number of divisors of X? In the explanation given - it says that X will be divisible by 5800-4864 Can someone explain how we can come up with this ?

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