Binary and decimal representations of integers divisibility

Binary and decimal representations of integers, divisibility tests Find the value of the digit x such that 2784x = x middot 5569 Find the values of the digits x and y such that 495|273x 49y5

Solution

Note first digit of 5569 is 5 and 2784x is a 5 digit number starting with 2

So, x can be 4 or 5

If x is 4 then last digit of 5569 would be 6

if x is 5 last digit of 5569 would be 5

Hene, x=5

Check:

5569*5=27845