Question

Factor 20p–90q.
Write your answer as a product with a whole number greater than 1.

Answer 1

To factor the expression \( 20p - 90q \), we first look for the greatest common factor (GCF) of the two terms, \( 20p \) and \( 90q \).

1. **Find the GCF**:
- The GCF of the coefficients \( 20 \) and \( 90 \) can be found by listing the factors:
- Factors of \( 20 \) are \( 1, 2, 4, 5, 10, 20 \).
- Factors of \( 90 \) are \( 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 \).
- The common factors are \( 1, 2, 5, 10 \), and the greatest among them is \( 10 \).

2. **Factor out the GCF**:
- Now we can factor out \( 10 \):
\[
20p - 90q = 10(2p - 9q)
\]

Thus, the factored form of \( 20p - 90q \) is:
\[
\boxed{10(2p - 9q)}
\]