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.