Question

Identify the greatest common factor of 50b and 25bcy

Answer 1

To find the greatest common factor (GCF) of the terms \(50b\) and \(25bcy\), we can break each term down into its factors.

1. **Factors of \(50b\)**:
- \(50 = 2 \times 25 = 2 \times 5^2\)
- So, \(50b = 2 \times 5^2 \times b\)

2. **Factors of \(25bcy\)**:
- \(25 = 5^2\)
- So, \(25bcy = 5^2 \times b \times c \times y\)

Now, we identify the common factors between \(50b\) and \(25bcy\):

- For the coefficients \(50\) and \(25\):
- The GCF of \(50\) and \(25\) is \(25\).

- For the variable \(b\):
- Both terms have \(b\), so the common factor is \(b\).

- The expression \(c \times y\) in \(25bcy\) does not contribute to the GCF, as there is no corresponding \(c\) or \(y\) in \(50b\).

Combining these common factors, we have:

\[
\text{GCF} = 25 \times b = 25b
\]

Thus, the greatest common factor of \(50b\) and \(25bcy\) is \(\boxed{25b}\).