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The rule to decide if a number is divisible by 9 is to look at the sum of the digits. If the sum of the digits is divisible by 9, then so is the number.
A number is divisible by 3 if the sum of its digits is a multiple of 3. A number is divisible by 6 if the sum of its digits is a multiple of 3 and it's even. A number is divisible by 9 if the sum of its digits is a multiple of 9.
If the sum of its digits add up to 9
Check the sum of the digits, if the sum divisible by 3 then the number is divisible by 3. Example 910: the sum of digits= 9 + 1 + 0 = 10, but 10 is not divisible by 3, so the number 910 is not divisible by 3. Example 2154: the sum of digits = 2 + 1 + 5 + 4 = 12, this sum is divisible by 3, so the number 2154 is divisible by 3. if the sum is long you can check the sum of the sum and apply the same rule. Example 52498731: the sum of digits = 5 + 2 + 4 + 9 + 8 + 7 + 3 + 1 = 39, the sum of the digits for 39 = 3 + 9 = 12, so the original number, i.e. 52498731 is divisible by 3.
Any even number divisible by 9, if the sum of the digits is divisible by 9. If it's an even number divisible by 9, it's divisible by 18.