Find the HCF (Highest common factor) of the given numbers 15a²b² and -24ab.

To find the Highest Common Factor (HCF) of the expressions 15a²b² and -24ab, we need to break down each term into its prime factors and variables.

Step 1: Factor the Coefficients

First, let's factor the numerical coefficients:

• 15 can be factored into 3 × 5.
• -24 can be factored into -1 × 2³ × 3.

Step 2: Identify the Variables

Next, we look at the variables:

• In 15a²b², the variables are a² and b².
• In -24ab, the variables are a and b.

Step 3: Determine the HCF of the Coefficients

The common factor of the coefficients 15 and -24 is 3, as it is the largest number that divides both.

Step 4: Determine the HCF of the Variables

For the variables:

• The HCF of a² and a is a.
• The HCF of b² and b is b.

Final Calculation

Now, we combine the HCF of the coefficients and the variables:

The HCF of 15a²b² and -24ab is:

3ab

This means that 3ab is the highest common factor of the given expressions.