Identify the GCF of 10x⁴y³ - 5x³y² + 20x²y.

Solution:

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 without leaving any remainder. To calculate GCF, there are three common ways- division, multiplication, and prime factorization.

To identify the GCF of 10x⁴y³, - 5x³y² and 20x²y,

10x⁴y³ = 2 × 5 × x × x × x × x × y × y × y

- 5x³y² = (-1) × 5 × x × x × x × y × y

20x²y = 2 × 2 × 5 × x × x × y

Collecting the highest common factors we get GCF = 5 × x × x × y = 5x²y

Example: Let us find the greatest common factor of 18a²b²c² and 27a³b³c³.

Solution: Given, 18a²b²c² and 27a³b³c³

Factors of 18a²b²c² = 2 × 3 × 3 × a × a × b × b × c × c

Factors of 27a³b³c³ = 3 × 3 × 3 × a × a × a × b × b × b × c × c × c

Collecting the highest common factors we get GCF = 3 × 3 × a × a × b × b × c × c = 9a²b²c²

Identify the GCF of 10x⁴y³ - 5x³y² + 20x²y.

Summary:

The GCF of 10x⁴y³, - 5x³y² and 20x²y is = 5x²y