Divisibility of nine

How do we find out that a whole number is divisible by nine? It's similar to divisibility by three: a number is divisible by nine if its digit sum is divisible by nine. The digit sum is the sum of all the digits of the number. Example:

• Is 78 705 divisible by nine? Its digit sum is 7 + 8 + 7 + 0 + 5 = 27. The number 27 is divisible by nine, so the number 78 705 is also divisible by nine.
• Is the number 11 288 divisible by nine? The numerical sum tells us 1 + 1 + 2 + 8 + 8 = 20 and since 20 is not divisible by nine, neither is 288 divisible by nine.

If necessary, we can do the numerical addition more than once. For example, is the number 7,606,373,886 divisible by nine? The numerical sum tells us 7 + 6 + 0 + 6 + 3 + 7 + 3 + 8 + 8 = 54. If we forget whether 54 is divisible by nine, we can do another numerical sum: 5 + 4 = 9, which shows that 54 is divisible by nine and therefore 7 606 373 886 is divisible by nine.