Math and Arithmetic
Factoring and Multiples

# Can 3 always be divisible by 9 but divisible by 6?

567 ###### 2012-03-01 14:10:16

Multiples of 9 and 6 are also divisible by three, the reverse is not true.

15 is divisible by 3, but not 6 or 9.

27 is divisible by 3 and 9, but not 6.

12 is divisible by 3 and 6, but not 9.

54 is divisible by 3, 6 and 9.

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## Related Questions No, 9 is divisible by 3 and 9, but not six 3 x 9 = 27, also not divisible by 6 72,344 is not evenly divisible by 3 or by 6 or by 9. All numbers divisible by 9 are divisible by 3; since 9 = 3 x 3 all multiples of 9 are also multiples of 3. However, all numbers divisible by 3 are not divisible by 9, eg 6 = 2 x 3 but 6 is not divisible by 9 (since 6 is not a multiple of 9) - it only takes one counter example to disprove a theory. 42 is divisible by 2, 3 and 6 but not by 9. 1350 is divisible by all of the numbers of 3, 6 and 9 All numbers divisible by 3 are NOT divisible by 9. As an example, 6, which is divisible by 3, is not divisible by 9. However, all numbers divisible by 9 are also divisible by 3 because 9 is divisible by 3.  Using the tests for divisibility:Divisible by 3:Add the digits and if the sum is divisible by 3, so is the original number: 2 + 3 + 4 = 9 which is divisible by 3, so 234 is divisible by 3Divisible by 6:Number is divisible by 2 and 3: Divisible by 2:If the number is even (last digit divisible by 2), then the whole number is divisible by 2. 234 is even so 234 is divisible by 2.Divisible by 3:Already shown above to be divisible by 3. 234 is divisible by both 2 & 3 so 234 is divisible by 6Divisible by 9:Add the digits and if the sum is divisible by 9, so is the original number: 2 + 3 + 4 = 9 which is divisible by 9, so 234 is divisible by 9Thus 234 is divisible by all 3, 6 & 9. Using the tests for divisibility:Divisible by 3:Add the digits and if the sum is divisible by 3, so is the original number: 6 + 8 + 4 = 18 which is divisible by 3, so 684 is divisible by 3Divisible by 6:Number is divisible by 2 and 3: Divisible by 2:If the number is even (last digit divisible by 2), then the whole number is divisible by 2. 684 is even so 684 is divisible by 2.Divisible by 3:Already shown above to be divisible by 3. 684 is divisible by both 2 & 3 so 684 is divisible by 6Divisible by 9:Add the digits and if the sum is divisible by 9, so is the original number: 6 + 8 + 4 = 18 which is divisible by 9, so 684 is divisible by 9Thus 684 is divisible by all 3, 6 & 9. yes. 2 + 1 + 6 = 9 9 is divisible by 3 so 216 is divisible by 3. Because 9 is divisible by 3, this is like the rule where if a number is divisible by 2 and 3 it is also divisible by 6. No, because when something is divisible by 6, it is divisible by 2 or 3. This is divisible by 3, but not 2.  1, 2, 7, 3 and 6 are not divisible by 4 and/or 9. 12736 is divisible by 4 but not by 9.  not divisible by 9.but it is divisible by 4.  No. For example, 9 is divisible by 3 and 9, but not 6. Even numbers that are divisble by 3 and 9 are also divisble by 6. To check for divisibility by 9 sum the digits of the number and if this sum is divisible by 9 then so is the original number. For 32643: 3 + 2 + 6 + 4 + 3 = 18 which is divisible by 9 so 32643 is divisible by 9. As 9 = 3 &times; 3, any number divisible by 9 is also divisible by 3, thus as 32643 is divisible by 9 it is also divisible by 3. However, for completeness: to check for divisibility by 3 sum the digits of the number and if this sum is divisible by 3 then so is the original number. For 32643: 3 + 2 + 6 + 4 + 3 = 18 which is divisible by 3 so 32643 is divisible by 3. No. 1+9+6=16, which is not divisible by 3; 1+4+6=11, which isn't divisible by 3 either. No. 1+9+6=16, which is not divisible by 3; 1+4+6=11, which isn't divisible by 3 either.  434 is evenly divisible by 2.It is not evenly divisible by 3, 6, or 9.  72,344 is evenly divisible by 2, but not by 3, 6, 9, 5, or 10. Your numbers appear to be mixed up because 20007 is divisible by 3 and 9 but not by 6 which is not one of its factors

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