| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | B. 12 |
B |
| deepseekr1 | The question asks for the number of positive and negative integers that 12 is a multiple of. This translates to finding all divisors of 12, both positive and negative. The positive divisors of 12 are: 1, 2, 3, 4, 6, 12 (6 numbers). The negative divisors are: -1, -2, -3, -4, -6, -12 (another 6 numbers). Adding these, there are **12 total integers** (6 positive + 6 negative). The answer options include B. 12, which matches this count. **Answer:** B. |
B |
| gpto1 | B | B |
| GPT-4o | D. 6 | B |
| llama3.1-70B-Instruct | Answer: B The positive integers that 12 is a multiple of are 1, 2, 3, 4, 6, and 12. The negative integers that 12 is a multiple of are –1, –2, –3, –4, –6, and –12. Thus, there are 12 positive and negative integers that 12 is a multiple of.Choice A is incorrect and may result from counting only the positive integers that 12 is a multiple of. Choice C is incorrect and may result from counting only the positive integers that are factors of 12. Choice D is incorrect and may result from counting only the positive integers that are factors of 12. The best answer is B. |
B |
| llama3.1-405B-Instruct | The positive integers that $12$ is a multiple of are $1, 2, 3, 4, 6,$ and $12$. The negative integers that $12$ is a multiple of are $-1, -2, -3, -4, -6,$ and $-12$. Therefore, the number of positive and negative integers that $12$ is a multiple of is $6+6=\boxed{12}$. The best answer is B. |
B |
| DeepSeek-Coder-V2 | C | B |
| Qwen2-72B-Instruct | D. 6 The positive divisors of 12 are 1, 2, 3, 4, 6, and 12. The negative divisors are -1, -2, -3, -4, -6, and -12. So there are 6 positive and 6 negative integers that 12 is a multiple of, but the question seems to be asking for the unique count, which is 6. |
B |
| baichuan4 | D | B |
| doubao | D. 6. The positive factors of 12 are 1, 2, 3, 4, 6, 12, and the negative factors are -1, -2, -3, -4, -6, -12, so there are 6 positive and negative integers that 12 is a multiple of. | B |
| minimax | To determine how many positive and negative integers 12 is a multiple of, we need to consider both the positive and negative divisors of 12. The positive divisors of 12 are: 1, 2, 3, 4, 6, and 12. For each positive divisor, there is a corresponding negative divisor that is also a multiple of 12: -1, -2, -3, -4, -6, and -12. So, we have 6 positive divisors and 6 negative divisors, making a total of 12 divisors when considering both positive and negative integers. The correct answer is: B. 12 |
B |
| kimi | A. 3 | B |
| wenxinyiyan | D Explanation: To find the positive and negative integers of which $12$ is a multiple, we consider the divisors of $12$. The positive divisors of $12$ are: $1, 2, 3, 4, 6, 12$. Since we are also considering negative integers, we include the negatives of these divisors: $-1, -2, -3, -4, -6, -12$. Therefore, there are a total of $6$ positive and $6$ negative integers of which $12$ is a multiple, giving a total of $12$ integers. However, the question asks for distinct positive and negative integers, so we count each divisor once, either in its positive or negative form. This gives us $6$ distinct integers. Hence the answer is D. $6$. |
B |
| zhipu | To determine how many positive and negative integers 12 is a multiple of, we need to list the factors of 12, considering both positive and negative factors. The factors of 12 are: \[ 1, 2, 3, 4, 6, 12 \] Each of these positive factors has a corresponding negative factor: \[ -1, -2, -3, -4, -6, -12 \] Thus, the total number of factors, both positive and negative, is: \[ 6 \text{ (positive factors)} + 6 \text{ (negative factors)} = 12 \] However, the question asks for the number of unique positive and negative integers that 12 is a multiple of, which implies considering each factor once. Therefore, the total number of positive and negative integers 12 is a multiple of is 6 (since each positive factor has a corresponding negative factor, but we count them together). So, the correct answer is: D. 6 |
B |
| gpto1 | B | B |
| deepseekv3 | To determine how many positive and negative integers \( 12 \) is a multiple of, we need to find all the integers that divide \( 12 \) without leaving a remainder. ### Step 1: Find the Positive Divisors of 12 The positive divisors of \( 12 \) are the numbers that divide \( 12 \) exactly. These are: \[ 1, 2, 3, 4, 6, 12 \] So, there are **6 positive divisors**. ### Step 2: Find the Negative Divisors of 12 For every positive divisor, there is a corresponding negative divisor. Thus, the negative divisors of \( 12 \) are: \[ -1, -2, -3, -4, -6, -12 \] So, there are **6 negative divisors**. ### Step 3: Calculate the Total Number of Divisors Adding the positive and negative divisors together: \[ 6 \text{ (positive)} + 6 \text{ (negative)} = 12 \text{ divisors} \] However, the question asks for **how many integers** \( 12 \) is a multiple of, not the total number of divisors. Since \( 12 \) is a multiple of each of its divisors, the total number of such integers is the same as the total number of divisors. ### Final Answer \[ \boxed{B} \] **Answer:** B |
B |