What is a counterexample for the conjecture?
Conjecture: Any number that is divisible by 3 is also divisible by 6.
(1 point)
Responses
12
30
26
9
The counterexample for the conjecture would be the number 9. It is divisible by 3, but not by 6.
To find a counterexample for the conjecture that any number divisible by 3 is also divisible by 6, we need to identify a number that is divisible by 3 but not by 6. An example of such a number is 9.
9 is divisible by 3 because 9 divided by 3 equals 3 with no remainder. However, 9 is not divisible by 6 because 9 divided by 6 equals 1 with a remainder of 3.
Therefore, 9 is a counterexample to the conjecture.
To find a counterexample for the given conjecture that any number divisible by 3 is also divisible by 6, we need to find a number that is divisible by 3 but not divisible by 6.
To be divisible by 3, a number must have a sum of its digits that is divisible by 3. Let's start by checking the potential counterexamples provided:
- 12: The sum of the digits is 1+2=3, which is divisible by 3. Now, we need to check if it is divisible by 6. Since 12 can be divided evenly by 6, it does not serve as a counterexample.
- 30: The sum of the digits is 3+0=3, which is divisible by 3. Now, we need to check if it is divisible by 6. Since 30 can be divided evenly by 6, it also does not serve as a counterexample.
- 26: The sum of the digits is 2+6=8, which is not divisible by 3. Hence, it is not divisible by 3 and can therefore be a potential counterexample.
- 9: The sum of the digits is 9, which is divisible by 3. Now, we need to check if it is divisible by 6. Since 9 cannot be divided evenly by 6, it serves as a counterexample to the conjecture.
Therefore, the counterexample for the conjecture "Any number that is divisible by 3 is also divisible by 6" is the number 9.