show that the number 26753298 is divisible by both 6 and 11

To show that the number \(26,753,298\) is divisible by both 6 and 11, we need to check the divisibility rules for 6 and 11.

### 1. Divisibility by 6
A number is divisible by 6 if it is divisible by both 2 and 3.

#### **Divisibility by 2**:
A number is divisible by 2 if its last digit is even. The last digit of \(26,753,298\) is 8, which is even. So, the number is divisible by 2.

#### **Divisibility by 3**:
A number is divisible by 3 if the sum of its digits is divisible by 3. Let's calculate the sum of the digits:
\[
2 + 6 + 7 + 5 + 3 + 2 + 9 + 8 = 42
\]
Now, check if 42 is divisible by 3:
\[
42 \div 3 = 14
\]
Since 42 is divisible by 3, \(26,753,298\) is divisible by 3.

Since \(26,753,298\) is divisible by both 2 and 3, it is divisible by 6.

### 2. Divisibility by 11
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is either 0 or divisible by 11.

Let's check the sums:
- **Sum of digits in odd positions** (from left to right): \(2 + 7 + 3 + 9 + 8 = 29\)
- **Sum of digits in even positions**: \(6 + 5 + 2 + 2 = 15\)

Now, find the difference between these sums:
\[
29 - 15 = 14
\]
Since 14 is not divisible by 11, \(26,753,298\) is **not** divisible by 11.

### Conclusion:
\(26,753,298\) is divisible by 6 but **not** by 11.

Do you have any questions, or would you like further explanation?

Here are 5 related questions to consider:
1. How do the divisibility rules for 2, 3, and 11 compare?
2. What happens if a number is divisible by 2 but not by 3?
3. How can you quickly check if a large number is divisible by 6?
4. What is a shortcut for checking divisibility by 11?
5. Can a number be divisible by 11 but not by 6?

**Tip:** When checking divisibility by 11, always remember to alternate adding and subtracting the digits to get the correct difference.

Learn how to show that the number 26753298 is divisible by 6 but not by 11 using divisibility rules and calculations. Understand the rules for divisibility by 2, 3, and 11, and how to apply them to determine divisibility of large numbers. Suitable for students in Grades 6-8.

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