Question

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

-5xy
-15x3y
-45x3y5
-75x5y7

Answer 1

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).

Answer 2

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

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*4*\ x^3*\ y^6*\ y\\45x^5y^5=15*3*\ x^3*\ x^2*\ y^2*\ y^3\\75x^3y=15*5*\ x^3*y`

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

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