Discussion
The number 42573* must be divisible by 72. What is the value of *?
Answer: C
For a number to be divisible by 72, it must be divisible by 8 and 9.
1. Divisibility by 8: The number formed by the last three digits, 73*, must be divisible by 8. Let's test values for *. 730 is not. 731 is not. 732 is not. 733 is not. 734 is not. 735 is not. 736 is. \(736 \div 8 = 92\). So, the missing digit * must be 6.
2. Divisibility by 9: Let's confirm with this value. The number is 425736. The sum of digits is \(4+2+5+7+3+6 = 27\). Since 27 is divisible by 9, the number is divisible by 9. Since it satisfies both conditions, the value of * is 6.
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