To find the greatest common factor (GCF) of the numbers 66, 44, and 22, we can first determine the prime factorization of each number.
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Prime Factorization:
- For 66: \[ 66 = 2 \times 3 \times 11 \]
- For 44: \[ 44 = 2^2 \times 11 \]
- For 22: \[ 22 = 2 \times 11 \]
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Identify Common Prime Factors: The common prime factors of all three numbers are:
- \(2\)
- \(11\)
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Determine the Lowest Powers:
- The lowest power of \(2\) in the factorizations is \(2^1\).
- The lowest power of \(11\) is \(11^1\).
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Calculate the GCF: The GCF is the product of the common prime factors raised to the lowest powers: \[ \text{GCF} = 2^1 \times 11^1 = 2 \times 11 = 22 \]
Therefore, the greatest common factor of 66, 44, and 22 is \( \boxed{22} \).