The question asks us to identify which of the given numbers divides 747579723.

Divisibility Check for 747579723

We need to test the divisibility of the number 747579723 by the options provided: 9, 13, 8, and 11.

Testing Divisibility by 11

The rule for divisibility by 11 is that the alternating sum of the digits must be divisible by 11.

For the number 747579723, the alternating sum is calculated as:

$ (7 - 4) + (7 - 5) + (7 - 9) + (7 - 2) + 3 $

Let's calculate step-by-step:

• First pair: $7 - 4 = 3$
• Second pair: $7 - 5 = 2$
• Third pair: $7 - 9 = -2$
• Fourth pair: $7 - 2 = 5$
• Last digit: $3$

Summing these results:

$ 3 + 2 + (-2) + 5 + 3 = 11 $

Since the result, 11, is divisible by 11, the number 747579723 is divisible by 11.

Checking Other Options

Let's briefly check the divisibility by 8 and 9.

• Divisibility by 8: The rule requires the last three digits (723) to be divisible by 8. Since $723 \div 8 = 90.375$, 723 is not divisible by 8.
• Divisibility by 9: The rule requires the sum of the digits to be divisible by 9. The sum is $7 + 4 + 7 + 5 + 7 + 9 + 7 + 2 + 3 = 51$. Since 51 is not divisible by 9 ($51 \div 9 \approx 5.67$), the number is not divisible by 9.

Since 11 correctly divides 747579723 based on the divisibility rule, it is the correct answer.