To find the greatest common factor (GCF) of the numbers 5050 and 25, we can start by finding the prime factorization of each number.
First, we factor 25: \[ 25 = 5 \times 5 = 5^2 \]
Next, we factor 5050: \[ 5050 = 505 \times 10 \] Since \(10 = 2 \times 5\), we need to factor 505 further: \[ 505 = 101 \times 5 \] Thus, we have: \[ 5050 = 101 \times 5 \times 2 \times 5 = 101 \times 2 \times 5^2 \]
Now we can summarize the prime factorizations:
- 25 = \(5^2\)
- 5050 = \(101 \times 2 \times 5^2\)
To find the GCF, we take the minimum power of the common prime factors. The only prime factor common to both 25 and 5050 is 5. Both numbers have \(5^2\).
Thus, the GCF is: \[ 5^2 = 25 \]
In conclusion, the greatest common factor of 5050 and 25 is: \[ \boxed{25} \]
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