To find the greatest common factor (GCF) of the numbers 12, 28, and 4, we can start by determining the prime factorization of each number.
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Prime Factorization:
- \( 12 = 2^2 \times 3 \)
- \( 28 = 2^2 \times 7 \)
- \( 4 = 2^2 \)
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Identifying Common Factors: The common prime factors among these numbers are \( 2 \). To find the GCF, we take the lowest power of the common prime factors.
The common factor \( 2 \) appears in each factorization with the exponent \( 2 \):
- For \( 12 \): \( 2^2 \)
- For \( 28 \): \( 2^2 \)
- For \( 4 \): \( 2^2 \)
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Calculating the GCF: Therefore, the GCF is: \[ 2^2 = 4 \]
Thus, the greatest common factor of 12, 28, and 4 is \( \boxed{4} \).