Examine the following number for divisibility by 6:
217944

Answer

To determine whether the number 217944 is divisible by 6, we need to check if it is divisible by both 2 and 3.

### Step 1: Check for divisibility by 3
To check if a number is divisible by 3, we need to find the sum of its digits and see if that sum is divisible by 3.

- The digits of 217944 are: 2, 1, 7, 9, 4, and 4.
- Calculate the sum of the digits:
\[ 2 + 1 + 7 + 9 + 4 + 4 = 27 \]

- Now, check if 27 is divisible by 3:
\[ 27 \div 3 = 9 \]
Since 9 is a whole number, 27 is divisible by 3.

**Conclusion for Step 1**: The number 217944 is divisible by 3.

### Step 2: Check for divisibility by 2
To check if a number is divisible by 2, we look at its last digit. If the last digit is even (0, 2, 4, 6, or 8), then the number is divisible by 2.

- The last digit of 217944 is 4.
- Since 4 is an even number, it is divisible by 2.

**Conclusion for Step 2**: The number 217944 is divisible by 2.

### Final Conclusion
Since 217944 is divisible by both 2 and 3, we can conclude that it is also divisible by 6.

**Final Answer**: Yes, the number 217944 is divisible by 6.

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