To find the greatest common factor (GCF) of the terms 4xy² and 20x²y⁴, we need to identify the factors of each term.
First, let’s break down each term into its prime factors:
- 4xy²: 4 can be factored as 2 × 2, so:
- 4xy² = 2 × 2 × x × y²
- 20x²y⁴: 20 can be factored as 2 × 2 × 5, so:
- 20x²y⁴ = 2 × 2 × 5 × x² × y⁴
Next, we identify the common factors:
- From 4xy², we have: 2², x¹, and y².
- From 20x²y⁴, we have: 2², 5¹, x², and y⁴.
The GCF is determined by taking the lowest power of all common factors:
- The lowest power of 2 is 2².
- The lowest power of x is x¹.
- The lowest power of y is y².
Putting it all together, the greatest common factor (GCF) is:
GCF = 2² × x¹ × y² = 4xy²
So, the greatest common factor of 4xy² and 20x²y⁴ is 4xy².