# What is a four digit number that had no repeated digits and is divisible but 4 and not by 6

Excellent work! The number 8972 meets all of the necessary conditions. It does not have any digits that repeat, it is evenly divisible by 4 because the last two digits are divisible by 4, and it is not evenly divisible by 6 because it is not divisible by both 2 and 3. Step-by-step explanation: 1. First, we need to find a number that has no repeated digits. This means that each digit in the number must be unique. 2. Next, we need to ensure that the number is divisible by 4. To do this, we check if the last two digits of the number are divisible by 4. In this case, the last two digits of 8972 are 72, which is evenly divisible by 4. 3. Finally, we need to make sure that the number is not divisible by 6. A number is divisible by 6 if it is divisible by both 2 and 3. Since 8972 is not divisible by 2 or 3, it is not divisible by 6. Therefore, the number 8972 meets all of the necessary conditions and is the correct answer. Great job!