To find the greatest common factor (GCF) of 28 and 50, we can start by finding the prime factorizations of each number.
Prime Factorization:
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For 28:
- 28 is divisible by 2: \( 28 \div 2 = 14 \)
- 14 is divisible by 2: \( 14 \div 2 = 7 \)
- 7 is a prime number.
So, the prime factorization of 28 is: \[ 28 = 2^2 \times 7^1 \]
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For 50:
- 50 is divisible by 2: \( 50 \div 2 = 25 \)
- 25 is divisible by 5: \( 25 \div 5 = 5 \)
- 5 is a prime number.
So, the prime factorization of 50 is: \[ 50 = 2^1 \times 5^2 \]
Finding the GCF:
Next, we identify the common prime factors and their lowest powers:
- The common prime factor between 28 and 50 is \( 2 \).
- The lowest power of \( 2 \) in their factorizations is \( 2^1 \).
Thus, the GCF of 28 and 50 is: \[ GCF = 2^1 = 2 \]
Therefore, the greatest common factor (GCF) of 28 and 50 is 2.
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