Final answer:
The highest common factor of 8x²y and 6y is 2y. This is found by factoring both expressions and identifying the common factors 2 and y.
Step-by-step explanation:
To find the highest common factor (HCF) of 8x²y and 6y, we need to factor each term and then find the common factors. First, we write out the prime factors:
- 8x²y = 2 × 2 × 2 × x × x × y
- 6y = 2 × 3 × y
Next, we identify the common factors between the two sets of prime factors. Here, we can see that 2 and y are common to both expressions.
Therefore, the highest common factor of 8x²y and 6y is 2y. So the correct answer is option (a). 2y.