How do you do divisibility by (3) three and (9) nine

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A number is divisible by 3 if the digits of the number add up to be a number divisible by 3.  So, 231,513 is divisible by 3 sonce 2+3+1+5+1+3 = 15 and 1+5 = 6.  6 is divisible by 3 and then so is 231,513. Same thing for 9 - if the numbers digits add up to be something divisible by 9, then the number is divisible by 9.  So, 6,405,939 is divisible by 9 since 6+4+0+5+9+3+9 = 36 and 3+6 = 9 and 9 is divisible by 9.  Yeah?