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Sagot :
Answer:
To determine whether each number is divisible by 4, 8, 11, and 12, we will apply the divisibility rules for each number:
1. **Divisibility by 4**: A number is divisible by 4 if the last two digits are divisible by 4.
2. **Divisibility by 8**: A number is divisible by 8 if the last three digits are divisible by 8.
3. **Divisibility by 11**: A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or divisible by 11.
4. **Divisibility by 12**: A number is divisible by 12 if it is divisible by both 3 and 4.
Let's check each number:
### 1. **188**
- **Divisible by 4**: Yes, \(88 \div 4 = 22\) ✔️
- **Divisible by 8**: No, \(188 \div 8 = 23.5\) ❌
- **Divisible by 11**: No, \((1 + 8) - 8 = 1 \) ❌
- **Divisible by 12**: No, it is not divisible by both 3 and 4 ❌
### 2. **248**
- **Divisible by 4**: Yes, \(48 \div 4 = 12\) ✔️
- **Divisible by 8**: Yes, \(248 \div 8 = 31\) ✔️
- **Divisible by 11**: No, \((2 + 8) - 4 = 6\) ❌
- **Divisible by 12**: No, it is not divisible by both 3 and 4 ❌
### 3. **322**
- **Divisible by 4**: No, \(22 \div 4 \neq \text{whole number}\) ❌
- **Divisible by 8**: No, \(322 \div 8 \neq \text{whole number}\) ❌
- **Divisible by 11**: No, \((3 + 2) - 2 = 3\) ❌
- **Divisible by 12**: No, it is neither divisible by 4 nor 3 ❌
### 4. **4132**
- **Divisible by 4**: Yes, \(32 \div 4 = 8\) ✔️
- **Divisible by 8**: Yes, \(132 \div 8 = 16.5 \) (wrongly taken only two digits, it's 4132: Yes, \(4132 \div 8 = 516.5\)) ❌
- **Divisible by 11**: No, \((4 + 3) - (1 + 2) = 4\) ❌
- **Divisible by 12**: No, because it is not divisible by both 3 and 4 ❌
### 5. **5264**
- **Divisible by 4**: Yes, \(64 \div 4 = 16\) ✔️
- **Divisible by 8**: Yes, \(264 \div 8 = 33 \times 8 \neq\) ❌
- **Divisible by 11**: Yes, \((5 + 6) - (2 + 4) = 5\) ❌
- **Divisible by 12**: No, it is neither divisible by 4 nor by 8 ❌
### Final Result:
| Number | Divisible by 4 | Divisible by 8 | Divisible by 11 | Divisible by 12 |
|:------:|:--------------:|:--------------:|:---------------:|:---------------:|
| 188 | ✔️ | ❌ | ❌ | ❌ |
| 248 | ✔️ | ✔️ | ❌ | ❌ |
| 322 | ❌ | ❌ | ❌ | ❌ |
| 4132 | ✔️ | ❌ | ❌ | ❌ |
| 5264 | ✔️ | ✔️ | ❌ | ❌ |
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