| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | D. 12 |
D |
| deepseekr1 | The greatest common factor (GCF) of 252 and 96 can be found using the Euclidean algorithm. 1. **252 ÷ 96** gives a remainder of 60. 2. **96 ÷ 60** gives a remainder of 36. 3. **60 ÷ 36** gives a remainder of 24. 4. **36 ÷ 24** gives a remainder of 12. 5. **24 ÷ 12** leaves no remainder. The last non-zero remainder is **12**, which is the GCF. Alternatively, using prime factorization: - **252 = 2² × 3² × 7** - **96 = 2⁵ × 3** Common factors with the lowest exponents: **2² × 3 = 4 × 3 = 12**. Answer: **D** |
D |
| gpto1 | D | D |
| GPT-4o | B. 24 | D |
| llama3.1-70B-Instruct | B |
D |
| llama3.1-405B-Instruct | D. 12 |
D |
| DeepSeek-Coder-V2 | B. 24 | D |
| Qwen2-72B-Instruct | D. 12 | D |
| baichuan4 | To find the greatest common factor (GCF) of 252 and 96, we need to determine the largest number that divides both numbers without leaving a remainder. First, let's break down both numbers into their prime factors: 252 = 2^2 * 3^2 * 7 96 = 2^5 * 3^1 * 5^1 Now, we take the smallest power of each prime number that appears in both numbers: 2^2 (since 2^2 is the smallest power of 2 that divides both numbers) 3^1 (since 3^1 is the smallest power of 3 that divides both numbers) There are no other common prime factors. So, the GCF of 252 and 96 is: 2^2 * 3^1 = 4 * 3 = 12 Therefore, the correct answer is: D. 12 |
D |
| doubao | B To find the greatest common factor of 252 and 96, we can factorize them. 252 = 2×2×3×3×7, and 96 = 2×2×2×2×2×3. The common factors are 2 and 3, and the highest power of 2 is 2×2 = 4 and the highest power of 3 is 1. So the greatest common factor is 2×2×3 = 12, but 24 is also a common factor and is greater than 12. |
D |
| minimax | To find the greatest common factor (GCF) of 252 and 96, we can use the prime factorization method or the Euclidean algorithm. I'll use prime factorization for this explanation. First, find the prime factors of each number: 252 = 2^2 * 3^2 * 7 96 = 2^5 * 3 The GCF is the product of the lowest powers of common prime factors: GCF = 2^min(2,5) * 3^min(2,1) * 7^min(1,0) GCF = 2^2 * 3^1 * 7^0 GCF = 4 * 3 * 1 GCF = 12 So the greatest common factor of 252 and 96 is 12. Answer: D. 12 |
D |
| kimi | To find the greatest common factor (GCF) of 252 and 96, we can use the prime factorization method. First, let's find the prime factors of each number: 252 = 2^2 * 3^2 * 7 96 = 2^5 * 3 Now, we take the lowest power of each prime factor that appears in both factorizations: GCF = 2^2 * 3 = 4 * 3 = 12 So the greatest common factor of 252 and 96 is 12. Answer: D. 12 |
D |
| wenxinyiyan | D Explanation: To find the greatest common factor (GCF) of 252 and 96, we can use the prime factorization method. Prime factorization of 252: $252 = 2 \times 2 \times 3 \times 3 \times 7 = 2^{2} \times 3^{2} \times 7$ Prime factorization of 96: $96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^{5} \times 3$ Now, to find the GCF, we take the common factors with the lowest exponents: $\text{GCF} = 2^{2} \times 3 = 4 \times 3 = 12$ Therefore, the greatest common factor of 252 and 96 is 12. So, the answer is D. |
D |
| zhipu | To find the greatest common factor (GCF) of 252 and 96, we can use the prime factorization method. First, let's find the prime factorization of each number: - 252: \( 252 \div 2 = 126 \) \( 126 \div 2 = 63 \) \( 63 \div 3 = 21 \) \( 21 \div 3 = 7 \) So, the prime factorization of 252 is \( 2^2 \times 3^2 \times 7 \). - 96: \( 96 \div 2 = 48 \) \( 48 \div 2 = 24 \) \( 24 \div 2 = 12 \) \( 12 \div 2 = 6 \) \( 6 \div 2 = 3 \) So, the prime factorization of 96 is \( 2^5 \times 3 \). Next, identify the common prime factors and their smallest exponents: - For 2: The smallest exponent is 2 (from \( 2^2 \) in 252). - For 3: The smallest exponent is 1 (from \( 3 \) in 96). Therefore, the GCF is \( 2^2 \times 3 = 4 \times 3 = 12 \). So, the correct answer is D. 12. |
D |
| gpto1 | D | D |
| deepseekv3 | To find the greatest common factor (GCF) of 252 and 96, we can use the **prime factorization** method. ### Step 1: Find the prime factors of each number. - **Prime factors of 252**: \(252 = 2 \times 126\) \(126 = 2 \times 63\) \(63 = 3 \times 21\) \(21 = 3 \times 7\) So, \(252 = 2^2 \times 3^2 \times 7\). - **Prime factors of 96**: \(96 = 2 \times 48\) \(48 = 2 \times 24\) \(24 = 2 \times 12\) \(12 = 2 \times 6\) \(6 = 2 \times 3\) So, \(96 = 2^5 \times 3\). ### Step 2: Identify the common prime factors with the smallest exponents. - Common prime factors: \(2\) and \(3\). - Smallest exponents: For \(2\), it's \(2^2\) (from 252). For \(3\), it's \(3^1\) (from 96). ### Step 3: Multiply these together to find the GCF. \(GCF = 2^2 \times 3 = 4 \times 3 = 12\). ### Final Answer: The greatest common factor of 252 and 96 is **12**. **Answer: D. 12** |
D |