To find the greatest common factor (GCF) of the numbers 5, 45, 50, and 10, we can start by determining the prime factorization of each number:
- 5: The prime factorization is \(5\) (since it is a prime number).
- 45: The prime factorization is \(3^2 \times 5\).
- 50: The prime factorization is \(2 \times 5^2\).
- 10: The prime factorization is \(2 \times 5\).
Next, we will list the prime factors for each number:
- 5: \(5\)
- 45: \(3^2, 5\)
- 50: \(2, 5^2\)
- 10: \(2, 5\)
Now, we identify the common prime factors across all these numbers. The only prime factor common to all four numbers is \(5\).
Next, we determine the lowest power of this common prime factor:
- The power of \(5\) in \(5\) is \(5^1\).
- The power of \(5\) in \(45\) is \(5^1\).
- The power of \(5\) in \(50\) is \(5^2\).
- The power of \(5\) in \(10\) is \(5^1\).
The lowest power is \(5^1 = 5\).
Thus, the greatest common factor of 5, 45, 50, and 10 is \(\boxed{5}\).
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