To find the greatest common factor (GCF) of 48 and 30, we can use the prime factorization method.
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Prime Factorization of 48:
- 48 can be divided by 2: \( 48 \div 2 = 24 \)
- 24 can be divided by 2: \( 24 \div 2 = 12 \)
- 12 can be divided by 2: \( 12 \div 2 = 6 \)
- 6 can be divided by 2: \( 6 \div 2 = 3 \)
- 3 is a prime number.
Thus, the prime factorization of 48 is: \[ 48 = 2^4 \times 3^1 \]
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Prime Factorization of 30:
- 30 can be divided by 2: \( 30 \div 2 = 15 \)
- 15 can be divided by 3: \( 15 \div 3 = 5 \)
- 5 is a prime number.
Thus, the prime factorization of 30 is: \[ 30 = 2^1 \times 3^1 \times 5^1 \]
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Finding the GCF: To find the GCF, we take the lowest power of each common prime factor from both factorizations:
- The common prime factors are 2 and 3.
- For 2: the minimum power is \( 2^1 \).
- For 3: the minimum power is \( 3^1 \).
Therefore, the GCF is: \[ GCF = 2^1 \times 3^1 = 2 \times 3 = 6 \]
Thus, the greatest common factor of 48 and 30 is \( \boxed{6} \).