Determine the number greater than 70 but less than 85 that is divisible by both 2 and 9.(1 point)
Responses
81
81
78
78
84
84
72
72
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To determine the number greater than 70 but less than 85 that is divisible by both 2 and 9, we can follow these steps:
1. Start with the lower limit, which is 71.
2. Check if this number is divisible by both 2 and 9.
- To check if a number is divisible by 2, we look at its units digit. If the units digit is 0, 2, 4, 6, or 8, the number is divisible by 2.
- To check if a number is divisible by 9, we sum up its digits. If the sum is divisible by 9, then the number is divisible by 9.
3. If the number is not divisible by both 2 and 9, increment it by 1 and repeat step 2.
4. Repeat steps 2 and 3 until we find a number that satisfies both divisibility rules.
Applying these steps to the given range (greater than 70 and less than 85):
- 71 is not divisible by 2 and 9.
- 72 is divisible by 2 (ends with a 2) but not by 9 (7 + 2 = 9).
- 73 is not divisible by 2 and 9.
- 74 is divisible by 2 (ends with a 4) but not by 9 (7 + 4 = 11).
- 75 is not divisible by 2 and 9.
- 76 is divisible by 2 (ends with a 6) but not by 9 (7 + 6 = 13).
- 77 is not divisible by 2 and 9.
- 78 is divisible by both 2 (ends with an 8) and 9 (7 + 8 = 15).
- 79 is not divisible by 2 and 9.
- 80 is divisible by 2 (ends with a 0) but not by 9 (8 + 0 = 8).
- 81 is divisible by both 2 (ends with a 2) and 9 (8 + 1 = 9).
- 82 is not divisible by 2 and 9.
- 83 is not divisible by 2 and 9.
- 84 is divisible by both 2 (ends with a 4) and 9 (8 + 4 = 12).
Therefore, the number greater than 70 but less than 85 that is divisible by both 2 and 9 is 78.