What is the greatest common factor of 60x⁴y⁷, 45x⁵y⁵, and 75x³y?

Solution:

The algebraic expressions given are

60x⁴y⁷, 45x⁵y⁵, and 75x³y

By using the prime factorization method and laws of exponents

60x⁴y⁷ = 3  × 5 × 4 × x³ × × x × y⁶ × y

45x⁵y⁵ = 3  × 5 × x³ × x² × y² × y²× y

75x³y = 3  × 5 × 5 × x³ × y

15 is the common coefficient and the common factor is x³y.

Therefore, the greatest common factor is 15x³y.

What is the greatest common factor of 60x⁴y⁷, 45x⁵y⁵, and 75x³y?

Summary:

The greatest common factor of 60x⁴y⁷, 45x⁵y⁵, and 75x³y is 15x³y.