To find the greatest common factor (GCF) of 24, 36, and 607, we can start by finding the prime factorization of the first two numbers, as 607 is a significantly larger number that is also a prime number.
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Prime factorization of 24:
- \( 24 = 2^3 \times 3^1 \)
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Prime factorization of 36:
- \( 36 = 2^2 \times 3^2 \)
Next, we'll find the GCF of 24 and 36.
- The GCF will take the lowest power of each prime factor present in both numbers:
- For \(2\), the lower power is \(2^2\).
- For \(3\), the lower power is \(3^1\).
So, the GCF of 24 and 36 is: \[ GCF(24, 36) = 2^2 \times 3^1 = 4 \times 3 = 12 \]
Now, we need to check if this GCF (12) is also a factor of 607. Since 607 is a prime number, its only factors are 1 and 607. Thus, we check if 12 is a factor of 607.
\[ 607 \div 12 \approx 50.5833 \quad (not\ an\ integer) \]
Since 12 is not a factor of 607, we consider the next lower potential GCF, which is to check factors of 12: Those factors are 1, 2, 3, 4, and 6.
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Check 6: \[ 607 \div 6 \approx 101.1667 \quad (not\ an\ integer) \]
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Check 4: \[ 607 \div 4 \approx 151.75 \quad (not\ an\ integer) \]
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Check 3: \[ 607 \div 3 \approx 202.3333 \quad (not\ an\ integer) \]
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Check 2: \[ 607 \div 2 = 303.5 \quad (not\ an\ integer) \]
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Check 1: \[ 607 \div 1 = 607 \quad (is\ an\ integer) \]
Thus, the only common factor among 24, 36, and 607 is 1.
Therefore, the greatest common factor of 24, 36, and 607 is 1, which means none of the choices (4, 6, 8, or 12) is correct. However, given the options provided, if these were hypothetical and did not include 1, we'd pick the largest of those that apply, which would be 12 due to GCF(24, 36).
But to clarify, the GCF for all three is indeed 1.