Verified Answer :

W0lf93

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).

JeanaShupp

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 =  \(15x^3y\)



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