# SOLUTION: Find digits a and b such that the number 34a47b5893 is divisible by 99.

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 Click here to see ALL problems on Divisibility and Prime Numbers Question 75181: Find digits a and b such that the number 34a47b5893 is divisible by 99.Answer by nilan(15)   (Show Source): You can put this solution on YOUR website!Suppose 34a47b5893 is divisible by 99 Then obviously it is divisible by 9 If a number is divisible by 9 the sum of all the digits should divisible by 9 (this can be easily proved) For example let the number abcd divisible by 9 then where k is positive integer Then then a+b+d+c is divisible by 9 This can be proved for any number (can be given a general proof. Try it) Again to the problem Then the sum of 34a47b5893 is divisible by 9 Then 3+4+a+4+7+b+5+8+9+3 is divisible by 9 Then 43+a+b is divisible by nine Then a=0 and b=2 Or a=2 and b = 0