What is the greatest common factor of 4xy² and 20x²y⁴?

Solution:

The process of finding the factors is called factoring.

All numbers have factors.

For example, 7 and 3 are the factors of 21.

Given 4xy² and 20x²y⁴

Factoring we get

4xy² = 2 × 2 × x × y × y

20x²y⁴  = 2 × 2 × 5 × x × x × y × y × y × y

Now grouping the common factors we get, 2 × 2 × x × y × y

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers.

The GCF of two natural numbers x and y is the largest possible number that divides both x and y. 

Therefore, the greatest common factor is 4xy²

What is the greatest common factor of 4xy² and 20x²y⁴?

Summary:

The greatest common factor of 4xy² and 20x²y⁴ is 4xy².