Question

Identify the greatest common factor of 25, w, squared, z25w
2
z and 25, b, cubed, c, y, squared25b
3
cy
2
.
Answer
Attempt 1 out of 5

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Answer 1

To identify the greatest common factor (GCF) of the two given expressions, we will break down each expression into its factors:

1. **First expression:** \( 25w^2z \)
- The number \( 25 \) can be factored as \( 5^2 \).
- The expression is \( 5^2 \cdot w^2 \cdot z \).

2. **Second expression:** \( 25b^3cy^2 \)
- Similarly, the number \( 25 \) can be factored as \( 5^2 \).
- The expression is \( 5^2 \cdot b^3 \cdot c \cdot y^2 \).

Now, we need to find the GCF by comparing the factorizations.

- The numerical part: The GCF of \( 5^2 \) and \( 5^2 \) is \( 5^2 \) (which is \( 25 \)).
- For variable \( w \): The GCF of \( w^2 \) (from the first expression) and there's no \( w \) in the second expression, thus it contributes \( 1 \) (no common factor).
- For variable \( z \): There is no \( z \) in the second expression, thus it also contributes \( 1 \).
- For variable \( b \): There is no \( b \) in the first expression, thus it contributes \( 1 \).
- For variable \( c \): There is no \( c \) in the first expression, giving it a contribution of \( 1 \).
- For variable \( y \): The first expression does not have \( y \), contributing \( 1 \).

Now, combine these factors:

\[
\text{GCF} = 25 \cdot 1 \cdot 1 \cdot 1 \cdot 1 = 25
\]

Thus, the greatest common factor of \( 25w^2z \) and \( 25b^3cy^2 \) is \(\boxed{25}\).