Question

Identify the greatest common factor of 5050 and 25, w25w.

Answer 1

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:
\[
\boxed{25}
\]