Question

Find the greatest common factor of these two expressions: 16v^6y^7w^8 and 28v^2y^7​.

a) 4v^2y^7
b) 8v^2y^7
c) 16v^6y^7w^8
d) 28v^6y^7w^8

Answer 1

To find the greatest common factor (GCF) of 16v^6y^7w^8 and 28v^2y^7, break down both expressions into their prime factors and identify the common factors. The GCF is the product of the common factors: 4v^2y^7.

Step-by-step explanation:

To find the greatest common factor (GCF) of 16v^6y^7w^8 and 28v^2y^7, we need to identify the common factors. First, let's break down both expressions into their prime factors:

16v^6y^7w^8 = 2^4 * v^6 * y^7 * w^8

28v^2y^7 = 2^2 * 7 * v^2 * y^7

Now, we can focus on the common prime factors, which are 2, v^2, and y^7. The GCF is the product of these common factors:

GCF = 2^2 * v^2 * y^7 = 4v^2y^7

Therefore, the correct answer is option a) 4v^2y^7.