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The given expression is \( 45a + 36b \). To factor this expression, we need to find the greatest common factor (GCF) of the two terms.

1. The factors of 45 are: \( 1, 3, 5, 9, 15, 45 \).
2. The factors of 36 are: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \).

The greatest common factor of 45 and 36 is \( 9 \).

So, we factor out 9 from the expression:

\[
45a + 36b = 9(5a + 4b)
\]

Thus, the factored form is:

\[
9(5a + 4b)
\]

Let me know if you'd like further details or have any questions.

Here are 5 related questions you can explore:
1. How do you find the greatest common factor (GCF) of two numbers?
2. What happens if one of the terms does not have a common factor greater than 1?
3. Can you factor an expression that involves more than two terms?
4. What is the difference between factoring by grouping and factoring the greatest common factor?
5. How do you know when an expression is fully factored?

**Tip**: Always check if there is a common factor in both numerical coefficients and variables before factoring an expression.

Factor 45a + 36b. Write your answer as a product with a whole number greater than 1.

Learn how to factor the algebraic expression 45a + 36b by finding the greatest common factor (GCF). This detailed step-by-step solution is ideal for students in Grades 6-8 and covers key algebraic concepts.

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