Question

The six digit number 54321.A is divisible by 9 where A is a single digit whole number.Find A

Answer 1

I'm assuming the number is 54321A instead of 54321.A

We could do guess and check. So replace A with 0 and see if 543210 is divisible by 9

543210/9 = 60,356.667 is not a whole number, so 543210 is not divisible by 9

Then replace A with 1 and see if it is a multiple of 9

543211/9 = 60,356.778 is not a whole number, so 543211 is not divisible by 9

This process might take a while. A shorter method is to add up the digits of 54321A to get 5+4+3+2+1+A = 15+A

The digits need to add up to some multiple of 9, so either 9 or 18 or 27, etc etc.

15+A = 9 solves to A = -6, we ignore this since A is a positive single digit number

15+A = 18 solves to A = 3, which is valid

Answer: A = 3