Question

If x and y are positive integers such that the greatest common factor of x^4y^6 and xy^5 is 96, then what does y equal?

a. 2
b. 3
c. 4
d. 6

Answer 1

The value of y is 5.

Step-by-step explanation:

To find the value of y, we need to determine the prime factors of the greatest common factor (GCF) of x^4y^6 and xy^5, which is 96.

Prime factorizing 96, we get 2^5 x 3.

Since the GCF is the product of common factors raised to the lowest power, we need to find the lowest power of y that appears in both expressions.

In x^4y^6, the lowest power of y is 6.

In xy^5, the lowest power of y is 5.

Therefore, the value of y is 5.