\[ 256 = 2^8 \]

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• The prime factorization of 48 is:
• \[ 48 = 2^4 \times 3^1 \]
• The prime factorization of 256 is:
• The GCD is found by taking the lowest power of all prime factors common to both numbers. Here, the only common prime factor is 2.
• For 2, the lowest power common to both factorizations is \(2^4\).
• Thus, the GCD of 48 and 256 is:

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