| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | To find the greatest common divisor (GCD) of the set \(\{704, -759, \frac{2683}{7}\}\), we need to follow these steps: 1. **Convert all numbers to integers**: Since the GCD is defined for integers, we need to convert \(\frac{2683}{7}\) to an integer. We can do this by multiplying all numbers by 7 to clear the fraction. \[ 704 \times 7 = 4928 \] \[ -759 \times 7 = -5313 \] \[ \frac{2683}{7} \times 7 = 2683 \] Now, we need to find the GCD of \(\{4928, -5313, 2683\}\). 2. **Remove the negative sign**: The GCD of a set of numbers is the same as the GCD of the set where all numbers are positive. So, we consider the set \(\{4928, 5313, 2683\}\). 3. **Find the GCD of the new set**: We use the Euclidean algorithm to find the GCD of the set \(\{4928, 5313, 2683\}\). - First, find the GCD of 4928 and 5313: \[ 5313 \div 4928 = 1 \quad \text{remainder} \quad 5313 - 4928 = 385 \] \[ 4928 \div 385 = 12 \quad \text{remainder} \quad 4928 - 12 \times 385 = 4928 - 4620 = 308 \] \[ 385 \div 308 = 1 \quad \text{remainder} \quad 385 - 308 = 77 \] \[ 308 \div 77 = 4 \quad \text{remainder} \quad 308 - 4 \times 77 = 308 - 308 = 0 \] So, \(\text{GCD}(4928, 5313) = 77\). - Next, find the GCD of 77 and 2683: \[ 2683 \div 77 = 34 \quad \text{remainder} \quad 2683 - 34 \times 77 = 2683 - 2618 = 65 \] \[ 77 \div 65 = 1 \quad \text{remainder} \quad 77 - 65 = 12 \] \[ 65 \div 12 = 5 \quad \text{remainder} \quad 65 - 5 \times 12 = 65 - 60 = 5 \] \[ 12 \div 5 = 2 \quad \text{remainder} \quad 12 - 2 \times 5 = 12 - 10 = 2 \] \[ 5 \div 2 = 2 \quad \text{remainder} \quad 5 - 2 \times 2 = 5 - 4 = 1 \] \[ 2 \div 1 = 2 \quad \text{remainder} \quad 2 - 2 \times 1 = 0 \] So, \(\text{GCD}(77, 2683) = 1\). Therefore, the greatest common divisor of \(\{704, -759, \frac{2683}{7}\}\) is \(\boxed{1}\). |
\frac{1}{7} |
| deepseek-r1 | To find the greatest common divisor (GCD) of the set \(\left\{704, -759, \frac{2683}{7}\right\}\), we need to consider the GCD of the numerators divided by the least common multiple (LCM) of the denominators. First, we convert all numbers to fractions with a common denominator of 7: - \(704 = \frac{704 \times 7}{7} = \frac{4928}{7}\) - \(-759 = \frac{-759 \times 7}{7} = \frac{-5313}{7}\) - \(\frac{2683}{7}\) remains as is. Next, we compute the GCD of the numerators 4928, -5313, and 2683. Using the Euclidean algorithm: 1. Compute \( \gcd(4928, 5313) \): - \(5313 \div 4928 = 1\) with remainder 385 - \(4928 \div 385 = 12\) with remainder 308 - \(385 \div 308 = 1\) with remainder 77 - \(308 \div 77 = 4\) with remainder 0 - Result: \(\gcd(4928, 5313) = 77\) 2. Compute \(\gcd(77, 2683)\): - \(2683 \div 77 = 34\) with remainder 65 - \(77 \div 65 = 1\) with remainder 12 - \(65 \div 12 = 5\) with remainder 5 - \(12 \div 5 = 2\) with remainder 2 - \(5 \div 2 = 2\) with remainder 1 - \(2 \div 1 = 2\) with remainder 0 - Result: \(\gcd(77, 2683) = 1\) Thus, the GCD of the numerators 4928, -5313, and 2683 is 1. The LCM of the denominators (1, 1, 7) is 7. Therefore, the GCD of the original set is \(\frac{1}{7}\). The greatest common divisor is \(\boxed{\dfrac{1}{7}}\). |
\frac{1}{7} |
| gpto1 | To find the greatest common divisor (GCD) of the set \(\{704, -759, \frac{2683}{7}\}\), we'll first address the fraction \(\frac{2683}{7}\) to work with integers. **Step 1: Convert all numbers to a common form** Let's write all numbers with a denominator of 7 to eliminate the fraction: 1. Multiply \(704\) by \(7\): \[704 \times 7 = 4928\] So, \(704 = \frac{4928}{7}\). 2. Multiply \(759\) by \(7\): \[759 \times 7 = 5313\] So, \(759 = \frac{5313}{7}\). Our numbers are now \(\frac{4928}{7},\ \frac{-5313}{7},\ \frac{2683}{7}\). **Step 2: Extract the numerators** Since the denominators are the same, we can focus on the numerators: \[ 4928,\ -5313,\ 2683 \] **Step 3: Find the GCD of the numerators** We'll use the Euclidean Algorithm to find the GCD. 1. Find \(\gcd(4928, 5313)\): \[ \gcd(5313, 4928) = \gcd(4928, 5313 - 4928 \times 1) = \gcd(4928, 385) \] \[ \gcd(4928, 385) = \gcd(385, 4928 - 385 \times 12) = \gcd(385, 308) \] \[ \gcd(385, 308) = \gcd(308, 385 - 308 \times 1) = \gcd(308, 77) \] \[ \gcd(308, 77) = \gcd(77, 308 - 77 \times 4) = \gcd(77, 0) = 77 \] 2. Find \(\gcd(77, 2683)\): \[ \gcd(2683, 77) = \gcd(77, 2683 - 77 \times 34) = \gcd(77, 65) \] \[ \gcd(77, 65) = \gcd(65, 77 - 65 \times 1) = \gcd(65, 12) \] \[ \gcd(65, 12) = \gcd(12, 65 - 12 \times 5) = \gcd(12, 5) \] \[ \gcd(12, 5) = \gcd(5, 12 - 5 \times 2) = \gcd(5, 2) \] \[ \gcd(5, 2) = \gcd(2, 5 - 2 \times 2) = \gcd(2, 1) \] \[ \gcd(2, 1) = \gcd(1, 2 - 1 \times 2) = \gcd(1, 0) = 1 \] **Step 4: Conclusion** Since \(\gcd(77, 2683) = 1\), the GCD of all three numerators is \(1\). Therefore, the greatest common divisor of the original set is \(\boxed{1}\). \(\boxed{1}\) |
\frac{1}{7} |
| gpt-4o-2024-08-06 | To find the greatest common divisor (GCD) of the set \(\{704, -759, \frac{2683}{7}\}\), we first need to simplify and consider the numbers involved. 1. **Simplify \(\frac{2683}{7}\):** Calculate \(\frac{2683}{7}\): \[ 2683 \div 7 = 383 \] So, \(\frac{2683}{7} = 383\). Now, the set of numbers is \(\{704, -759, 383\}\). 2. **Find the GCD of 704, 759, and 383:** We will use the Euclidean algorithm to find the GCD. - **GCD of 704 and 759:** Start with 704 and 759: \[ 759 = 704 \times 1 + 55 \] \[ 704 = 55 \times 12 + 44 \] \[ 55 = 44 \times 1 + 11 \] \[ 44 = 11 \times 4 + 0 \] The GCD of 704 and 759 is 11. - **GCD of 11 and 383:** Now find the GCD of 11 and 383: \[ 383 = 11 \times 34 + 9 \] \[ 11 = 9 \times 1 + 2 \] \[ 9 = 2 \times 4 + 1 \] \[ 2 = 1 \times 2 + 0 \] The GCD of 11 and 383 is 1. Thus, the greatest common divisor of the set \(\{704, -759, \frac{2683}{7}\}\) is \(\boxed{1}\). |
\frac{1}{7} |
| DeepSeek-Coder-V2-Lite-Instruct | To find the greatest common divisor (GCD) of the set \(\{704, -759, \frac{2683}{7}\}\), we will follow these steps: 1. **Convert the fraction to an integer**: \[ \frac{2683}{7} = 383.2857 \approx 383 \] Since we are dealing with integers, we will consider the integer part, which is 383. 2. **List the numbers**: \[ \{704, -759, 383\} \] 3. **Find the GCD of the absolute values**: \[ \text{GCD}(704, 759, 383) \] 4. **Use the Euclidean algorithm to find the GCD**: - First, find \(\text{GCD}(704, 759)\): \[ \text{GCD}(704, 759) = \text{GCD}(704, 759 \mod 704) \] \[ 759 \mod 704 = 55 \] \[ \text{GCD}(704, 55) = \text{GCD}(55, 704 \mod 55) \] \[ 704 \mod 55 = 39 \] \[ \text{GCD}(55, 39) = \text{GCD}(39, 55 \mod 39) \] \[ 55 \mod 39 = 16 \] \[ \text{GCD}(39, 16) = \text{GCD}(16, 39 \mod 16) \] \[ 39 \mod 16 = 7 \] \[ \text{GCD}(16, 7) = \text{GCD}(7, 16 \mod 7) \] \[ 16 \mod 7 = 2 \] \[ \text{GCD}(7, 2) = \text{GCD}(2, 7 \mod 2) \] \[ 7 \mod 2 = 1 \] \[ \text{GCD}(2, 1) = 1 \] So, \(\text{GCD}(704, 759) = 1\). - Next, find \(\text{GCD}(1, 383)\): \[ \text{GCD}(1, 383) = 1 \] 5. **Conclusion**: \[ \text{GCD}(704, 759, 383) = 1 \] Thus, the greatest common divisor of \(\{704, -759, \frac{2683}{7}\}\) is \(\boxed{1}\). |
\frac{1}{7} |
| Meta-Llama-3.1-405B-Instruct-Turbo | ## Step 1: First, we need to find the prime factorization of each number in the set. The prime factorization of 704 is $2^6 \cdot 11$, the prime factorization of -759 is $-3 \cdot 11 \cdot 23$, and the prime factorization of $\frac{2683}{7}$ is $7 \cdot 383$ but since it's a fraction, we should not include the 7 in the prime factorization, so we are left with 383. ## Step 2: Next, we need to find the common factors among the numbers in the set. Comparing the prime factorizations, we see that the only common prime factor is 11, but 383 is a prime number itself and 11 is not a factor of 383. ## Step 3: Since 11 is not a factor of 383, we need to look for common factors again. Upon reviewing the prime factorizations again, we see that there are no common prime factors among all three numbers. ## Step 4: Since there are no common prime factors among all three numbers, the greatest common divisor (GCD) is 1. This is because the only factor that all numbers have in common is 1. The final answer is: $\boxed{1}$ |
\frac{1}{7} |
| Meta-Llama-3.1-70B-Instruct-Turbo | ## Step 1: First, we need to find the prime factorization of each number in the set. We start by finding the prime factorization of 704, -759, and 2683/7. ## Step 2: Prime factorization of 704. The prime factorization of 704 is 2^6 * 11. ## Step 3: Prime factorization of -759. The prime factorization of -759 is -1 * 3 * 11 * 23. ## Step 4: Prime factorization of 2683/7. First, we simplify 2683/7 to get 383. The prime factorization of 383 is 383, which is a prime number. ## Step 5: Now, we need to find the greatest common divisor (GCD) of the three numbers. To find the GCD, we look for the highest power of each prime factor that appears in all three numbers. ## Step 6: Finding the GCD. The only common prime factor among the three numbers is 11. Therefore, the GCD is 11. The final answer is: $\boxed{11}$ |
\frac{1}{7} |
| Qwen2-72B-Instruct | To find the greatest common divisor (GCD) of the set $\{704, -759, \frac{2683}{7}\}$, we first need to ensure that all numbers are integers since the GCD is defined for integers. The number $\frac{2683}{7}$ is not an integer, but we can multiply all numbers by 7 to make them all integers without changing their GCD. Thus, we consider the GCD of $\{704 \times 7, -759 \times 7, 2683\}$. First, let's calculate these products: - $704 \times 7 = 4928$ - $-759 \times 7 = -5313$ - $2683$ remains unchanged Now, we have the set $\{4928, -5313, 2683\}$. We can ignore the negative sign when calculating the GCD, so we're looking for the GCD of $\{4928, 5313, 2683\}$. Let's use the Euclidean algorithm to find the GCD of these three numbers. First, we find the GCD of the first two numbers and then use that result to find the GCD with the third number. **Step 1: Find GCD(4928, 5313)** Using the Euclidean algorithm: - $5313 = 4928 \cdot 1 + 385$ - $4928 = 385 \cdot 12 + 308$ - $385 = 308 \cdot 1 + 77$ - $308 = 77 \cdot 4 + 0$ So, GCD(4928, 5313) = 77. **Step 2: Find GCD(77, 2683)** Again, using the Euclidean algorithm: - $2683 = 77 \cdot 34 + 65$ - $77 = 65 \cdot 1 + 12$ - $65 = 12 \cdot 5 + 5$ - $12 = 5 \cdot 2 + 2$ - $5 = 2 \cdot 2 + 1$ - $2 = 1 \cdot 2 + 0$ So, GCD(77, 2683) = 1. Therefore, the greatest common divisor of the original set $\{704, -759, \frac{2683}{7}\}$ is $\boxed{1}$. |
\frac{1}{7} |
| baichuan4 | To find the greatest common divisor (GCD) of a set of numbers, we can use the Euclidean algorithm or any other method that helps us identify the largest integer that divides all the numbers in the set without leaving a remainder. In this case, we have three numbers: 704, -759, and 2683/7. We should first simplify the third number by dividing it by 7: 2683 ÷ 7 = 383 Now, we have three numbers: 704, -759, and 383. It's important to note that the GCD of a set of numbers is not affected by the signs of the numbers. Therefore, we can ignore the negative sign of -759 and proceed as if it were positive. Next, we can use the Euclidean algorithm to find the GCD of 704 and 759. The Euclidean algorithm involves repeatedly dividing the larger number by the smaller number and then replacing the larger number with the remainder until the remainder is zero. The last non-zero remainder is the GCD. Let's apply the Euclidean algorithm: 759 ÷ 704 = 1 with a remainder of 55 704 ÷ 55 = 12 with a remainder of 44 55 ÷ 44 = 1 with a remainder of 11 44 ÷ 11 = 4 with a remainder of 0 Since the last non-zero remainder is 11, the GCD of 704 and 759 is 11. Now, we need to check if 11 also divides 383: 383 ÷ 11 = 34 with a remainder of 9 Since 11 does not divide 383 evenly, we conclude that the GCD of the set {704, -759, 383} is not 11. However, we notice that 11 is the largest number that divides both 704 and 759, and since 383 is not divisible by 11, we conclude that the GCD of the set is 1. Therefore, the greatest common divisor of the set {704, -759, 383} is 1. Final answer: $\boxed{1}$ |
\frac{1}{7} |
| doubao | First, convert $\frac{2683}{7}$ to a whole number: $\frac{2683}{7}=383$. Now find the greatest common divisor of 704, -759, and 383. Using the Euclidean algorithm: $704$ and $383$: $704=383\times1+321$ $383=321\times1+62$ $321=62\times5+11$ $62=11\times5+7$ $11=7\times1+4$ $7=4\times1+3$ $4=3\times1+1$ $3=1\times3$ So the greatest common divisor of 704 and 383 is 1. Now consider -759 and 1. The greatest common divisor of a number and 1 is always 1. So the greatest common divisor of the set is 1. $\boxed{1}$. |
\frac{1}{7} |
| gpto1 | To find the greatest common divisor (GCD) of the set \(\{704, -759, \frac{2683}{7}\}\), we'll first address the fraction \(\frac{2683}{7}\) to work with integers. **Step 1: Convert all numbers to a common form** Let's write all numbers with a denominator of 7 to eliminate the fraction: 1. Multiply \(704\) by \(7\): \[704 \times 7 = 4928\] So, \(704 = \frac{4928}{7}\). 2. Multiply \(759\) by \(7\): \[759 \times 7 = 5313\] So, \(759 = \frac{5313}{7}\). Our numbers are now \(\frac{4928}{7},\ \frac{-5313}{7},\ \frac{2683}{7}\). **Step 2: Extract the numerators** Since the denominators are the same, we can focus on the numerators: \[ 4928,\ -5313,\ 2683 \] **Step 3: Find the GCD of the numerators** We'll use the Euclidean Algorithm to find the GCD. 1. Find \(\gcd(4928, 5313)\): \[ \gcd(5313, 4928) = \gcd(4928, 5313 - 4928 \times 1) = \gcd(4928, 385) \] \[ \gcd(4928, 385) = \gcd(385, 4928 - 385 \times 12) = \gcd(385, 308) \] \[ \gcd(385, 308) = \gcd(308, 385 - 308 \times 1) = \gcd(308, 77) \] \[ \gcd(308, 77) = \gcd(77, 308 - 77 \times 4) = \gcd(77, 0) = 77 \] 2. Find \(\gcd(77, 2683)\): \[ \gcd(2683, 77) = \gcd(77, 2683 - 77 \times 34) = \gcd(77, 65) \] \[ \gcd(77, 65) = \gcd(65, 77 - 65 \times 1) = \gcd(65, 12) \] \[ \gcd(65, 12) = \gcd(12, 65 - 12 \times 5) = \gcd(12, 5) \] \[ \gcd(12, 5) = \gcd(5, 12 - 5 \times 2) = \gcd(5, 2) \] \[ \gcd(5, 2) = \gcd(2, 5 - 2 \times 2) = \gcd(2, 1) \] \[ \gcd(2, 1) = \gcd(1, 2 - 1 \times 2) = \gcd(1, 0) = 1 \] **Step 4: Conclusion** Since \(\gcd(77, 2683) = 1\), the GCD of all three numerators is \(1\). Therefore, the greatest common divisor of the original set is \(\boxed{1}\). \(\boxed{1}\) |
\frac{1}{7} |
| kimi | To find the greatest common divisor (GCD) of the numbers \(704\), \(-759\), and \(\frac{2683}{7}\), we will follow these steps: 1. **Convert all numbers to positive integers**: - \(704\) is already positive. - \(-759\) becomes \(759\). - \(\frac{2683}{7}\) is a fraction. First, we calculate its value: \[ \frac{2683}{7} = 383.2857 \quad (\text{not an integer}) \] This indicates there might be an error in the problem statement or interpretation. However, if we assume it should be an integer, let's consider the integer part \(383\) for further calculations. 2. **Find the prime factorizations**: - **Prime factorization of \(704\)**: \[ 704 \div 2 = 352 \\ 352 \div 2 = 176 \\ 176 \div 2 = 88 \\ 88 \div 2 = 44 \\ 44 \div 2 = 22 \\ 22 \div 2 = 11 \\ 11 \div 11 = 1 \] So, \(704 = 2^6 \times 11\). - **Prime factorization of \(759\)**: \[ 759 \div 3 = 253 \\ 253 \div 11 = 23 \\ 23 \div 23 = 1 \] So, \(759 = 3 \times 11 \times 23\). - **Prime factorization of \(383\)**: \(383\) is a prime number. 3. **Identify the common prime factors**: - The prime factors of \(704\) are \(2\) and \(11\). - The prime factors of \(759\) are \(3\), \(11\), and \(23\). - The prime factors of \(383\) are \(383\) (itself). The only common prime factor among all three numbers is \(11\). 4. **Determine the GCD**: Since \(11\) is the only common prime factor, the GCD of \(704\), \(759\), and \(383\) is \(11\). Therefore, the greatest common divisor is \(\boxed{11}\). |
\frac{1}{7} |
| minimax | To find the greatest common divisor (GCD) of the set $\{704, -759, \frac{2683}{7}\}$, we need to consider the GCD of the integers first, and then see if the fraction can be included. First, let's find the GCD of the two integers 704 and -759. Since the GCD of two numbers is the same as the GCD of their absolute values, we can ignore the sign and just consider 704 and 759. The Euclidean algorithm is a method for finding the GCD of two numbers. We repeatedly apply the algorithm until we get a remainder of 0. The last non-zero remainder is the GCD. Applying the Euclidean algorithm to 704 and 759: 1. Divide 759 by 704 to get a quotient and remainder: $$ 759 = 704 \cdot 1 + 55 $$ 2. Now divide 704 by the remainder 55: $$ 704 = 55 \cdot 12 + 44 $$ 3. Now divide 5 |
\frac{1}{7} |
| wenxinyiyan | 首先，我们需要将分数$\frac{2683}{7}$转换为整数，这样我们才能更容易地找到三个数的最大公约数。 将$\frac{2683}{7}$乘以7，得到： $\frac{2683}{7} \times 7 = 2683$ 现在，我们有三个整数：704, -759, 和 2683。为了找到它们的最大公约数，我们可以使用欧几里得算法。但首先，我们需要注意到-759是负数。在数学中，我们通常得到的最大公约数是非负数。因此，我们可以将-759转换为正数759，这样不会改变三个数的最大公约数。 接下来，我们应用欧几里得算法： 1. 比较704和759，我们发现759更大。因此，我们用759除以704，得到余数155。 2. 然后，我们用704除以155，得到余数42。 3. 接着，用155除以42，得到余数29。 4. 用42除以29，得到余数13。 5. 用29除以13，得到余数3。 6. 最后，用13除以3，得到余数1。然后，用3除以1，余数为0。 因此，704和759的最大公约数是1。 接下来，我们考虑第三个数2683。由于2683远大于704和759，并且我们已知704和759的最大公约数是1，所以我们可以直接得出704、-759和$\frac{2683}{7}$的最大公约数也是1。 所以，答案是：$\boxed{1}$。 |
\frac{1}{7} |
| zhipu | First, we ignore the negative sign on $-759$ since the greatest common divisor (GCD) will be the same for $759$ and $-759$. Next, we find the GCD of the integers in the set, which are $704$, $759$, and the numerator of the fraction, $2683$ (ignoring the denominator for now since it does not affect the GCD of the integers). We start by finding the GCD of $704$ and $759$: 1. **Prime Factorization of $704$:** - $704$ is even, so divide by $2$: $704 \div 2 = 352$ - $352$ is even, so divide by $2$: $352 \div 2 = 176$ - $176$ is even, so divide by $2$: $176 \div 2 = 88$ - $88$ is even, so divide by $2$: $88 \div 2 = 44$ - $44$ is even, so divide by $2$: $44 \div 2 = 22$ - $22$ is even, so divide by $2$: $22 \div 2 = 11$ - $11$ is a prime number. - Thus, $704 = 2^6 \cdot 11$. 2. **Prime Factorization of $759$:** - $759$ is not divisible by $2$ (it's odd). - Check divisibility by $3$: Sum of digits of $759$ is $7 + 5 + 9 = 21$, which is divisible by $3$. - $759 \div 3 = 253$ - $253$ is not divisible by $3$. - Check divisibility by $11$: $253 \div 11 = 23$ (since $253 = 11 \cdot 23$). - $23$ is a prime number. - Thus, $759 = 3 \cdot 11 \cdot 23$. The common prime factor between $704$ and $759$ is $11$. 3. **Check $2683$ for divisibility by $11$:** - $2683$ is not obviously divisible by $2$, $3$, or $5$. - Check divisibility by $11$: Alternating sum of digits $2 - 6 + 8 - 3 = 1$, not divisible by $11$. - However, we need to ensure no smaller common divisor exists, so we check $2683 \div 11 = 243.9$, not an integer. - Recheck smaller primes: $2683 \div 7 = 383$ (since $2683 = 7 \cdot 383$). - $383$ is a prime number. Since $2683$ does not share any common factors with $704$ and $759$ other than $1$, the GCD of the set $\{704, -759, \frac{2683}{7}\}$ is the GCD found earlier, which is $11$. Thus, the greatest common divisor of the set is $\boxed{11}$. |
\frac{1}{7} |
| deepseek-v3 | To find the **greatest common divisor (GCD)** of the set \(\{704, -759, \frac{2683}{7}\}\), we'll follow these steps: 1. **Understand the Elements:** - **704** and **-759** are integers. - \(\frac{2683}{7}\) is a rational number. 2. **Simplify the GCD Calculation:** - Since the GCD is typically defined for integers, we'll first find the GCD of the integers **704** and **-759**. - The sign doesn't affect the GCD, so we'll consider **704** and **759**. 3. **Apply the Euclidean Algorithm:** - **Step 1:** \(759 \div 704 = 1\) with a remainder of \(759 - 704 \times 1 = 55\). - **Step 2:** \(704 \div 55 = 12\) with a remainder of \(704 - 55 \times 12 = 44\). - **Step 3:** \(55 \div 44 = 1\) with a remainder of \(55 - 44 \times 1 = 11\). - **Step 4:** \(44 \div 11 = 4\) with a remainder of \(0\). The **last non-zero remainder** is **11**, so: \[ \gcd(704, 759) = 11 \] 4. **Include the Rational Number:** - To include \(\frac{2683}{7}\) in the GCD, consider its denominator. - Since **7** is a prime number and does not divide **11**, the GCD remains **11**. Therefore, the greatest common divisor of the set \(\{704, -759, \frac{2683}{7}\}\) is: \[ \boxed{11} \] |
\frac{1}{7} |