If a and b are both integers and a/b = 34.06 , what is the probability that the remainder of a/b is a multiple of 6?

I tried fixing some numbers and taking example but can’t proceed.

If a and b are both integers and a/b = 34.06 , what is the probability that the remainder of a/b is a multiple of 6?

I tried fixing some numbers and taking example but can’t proceed.

34.06 = 3406/100 = 1703/50

All the integers that will give 34.06 upon division can be obtained by multiplying an integer to 1703/50

multiplied by 1: 1703/50: r = 3

multiplied by 2: 3406/100: r = 6

multiplied by 3: 5109/150: r = 9

…

We can deduce that the remainder is 3 times the multiplication factor of 1703/50

6 = 3 x 2

So every second multiple of 3 is going to be a multiple of 6

Therefore, ans. 1/2