Check the divisibility of the given numbers, as indicated. Using tests for divisibility.
567126 by 6

Answer

To check if the number 567126 is divisible by 6, we need to follow the divisibility rules for both 2 and 3, since a number is divisible by 6 if it is divisible by both of these numbers.

### Step-by-Step Solution:

**Step 1: Check divisibility by 2**
- A number is divisible by 2 if its last digit is even.
- The last digit of 567126 is 6, which is even.

**Conclusion for Step 1:**
567126 is divisible by 2.

**Step 2: Check divisibility by 3**
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- Let's add the digits of 567126:
- 5 + 6 + 7 + 1 + 2 + 6 = 27

**Step 3: Check if the sum is divisible by 3**
- Now we need to check if 27 is divisible by 3.
- Since 27 divided by 3 equals 9 (which is a whole number), 27 is divisible by 3.

**Conclusion for Step 2:**
567126 is divisible by 3.

**Final Conclusion:**
Since 567126 is divisible by both 2 and 3, it is also divisible by 6.

### Summary:
- 567126 is divisible by 2 (last digit is even).
- The sum of the digits (27) is divisible by 3.
- Therefore, 567126 is divisible by 6.

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