Question

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

Answer 1

Answer:-The greatest common factor of  $60x^4y^7,\ 45x^5y^5\ and\ 75x^3y=15x^3y$

Step-by-step explanation:

Given algebraic expressions: $60x^4y^7,\ 45x^5y^5\ and\ 75x^3y$

Using prime factorization method and law of exponents, rewrite the expressions as

$60x^4y^7=15\times4\times\ x^3\times\ y^6\times\ y\\45x^5y^5=15\times3\times\ x^3\times\ x^2\times\ y^2\times\ y^3\\75x^3y=15\times5\times\ x^3\timesy$

We can see 15 is the common coefficient,and  is the common factor in the expressions

⇒The greatest common factor of =  $15x^3y$

Answer 2

The greatest common factor of two or more numbers is the greatest common factor of the two or more numbers that can divide the numbers without remainder. Factors of 60x^4y^7, 45x^5y^5 and 75x^3y. 60x^4y^7 = 2, 2, 3, 5, x, x, x, x, y, y, y, y, y, y, y 45x^5y^5 = 3, 3, 5, x, x, x, x, x, y, y, y, y, y 75x^3y = 3, 5, 5, x, x, x, y The common factors are 3, 5, x, x, x, y = 15x^3y (the second option).