# number 9

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 1224431.  Thu Feb 02, 2017 11:27 pm watched QI on numbers,was gutted to see they did not point out the magic of number9.As any number adding up to 9 is divisible by 9.i.e 4002001011 or 23022,8000001,6010101,

 1224614.  Fri Feb 03, 2017 3:01 pm Number 9... Number 9... Number 9... Number 9... Number 9... ...etc, etc, ad nauseum.

 1224940.  Sun Feb 05, 2017 11:27 pm In general, a number is divisible by N if and only if the sum of its digits written in base (N+1) is divisible by N. For example, 98 is divisible by 7 because 98 = 142 in base eight and 1+4+2 is divisible by 7. Also 135 is divisible by 15 because 135 = 87 in hexadecimal and 8+7 is divisible by 15.

 1225080.  Mon Feb 06, 2017 11:22 am Another fun thing about the number 9: Take any number. Rearrange its digits. Take the difference between the two numbers (subtract the smaller from the larger). This difference is always divisible by 9. E.g. Take 12345. Rearrange the digits to, say, 42513. Take the difference: 42513 − 12345 = 30168. 30168 is divisible by 9 – check it! The difference between two numbers such that the digits of one are those of the other rearranged is always divisible by 9. You can also try the same thing using N instead of 9 and permuting the digits in base N+1 instead of base ten. Example: Take 12345 in hexadecimal, which is 3039. Rearrange the digits to, say, 9033 in hexademal, which is 36915 in base ten. Take the difference: 36915 − 12345 = 24570. This time 24570 is divisible by 15. (The difference between two hexadecimal numbers such that the digits of one are those of the other rearranged is always divisible by 15.)

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