Which of the following numbers is divisible by 72?
- A23724128
- B24127812
- C35127918
- D22112136
Solution & Step-by-step Explanation
A number is divisible by 72 if it is completely divisible by both 8 and 9 (since 72=8×9 and gcd(8,9)=1).
Divisibility rule of 8: The last three digits must be divisible by 8.
Divisibility rule of 9: The sum of all digits must be divisible by 9.
Let's test option D (22112136):
Last 3 digits: 136. Since 136÷8=17, it is divisible by 8.
Sum of digits: 2+2+1+1+2+1+3+6=18. Since 18 is divisible by 9, the number is divisible by 9.
Since 22112136 satisfies both criteria, it is divisible by 72.
Divisibility rule of 8: The last three digits must be divisible by 8.
Divisibility rule of 9: The sum of all digits must be divisible by 9.
Let's test option D (22112136):
Last 3 digits: 136. Since 136÷8=17, it is divisible by 8.
Sum of digits: 2+2+1+1+2+1+3+6=18. Since 18 is divisible by 9, the number is divisible by 9.
Since 22112136 satisfies both criteria, it is divisible by 72.