Question

What is the GCF of 16a^3 b-8a^2 y

A.)8a
B.)8a^2
C.)2ab
D.)4a

what is the GCF???​

Answer 1

Answer:

B. option is correct (8a^2)

Answer 2

GCF :-

The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

given,

$16a^3 b-8a^2 y\\\mathrm{The\:roots\:are\:the\:intercepts\:with\:the\:x-axis}\:\left(y=0\right)\\16a^3b-8a^2y=0\\\mathrm{Subtract\:}16a^3b\mathrm{\:from\:both\:sides}\\16a^3b-8a^2y-16a^3b=0-16a^3b\\-8a^2y=-16a^3b\\\mathrm{Divide\:both\:sides\:by\:}-8a^2;\quad \:a\ne \:0\\\frac{-8a^2y}{-8a^2}=\frac{-16a^3b}{-8a^2};\quad \:a\ne \:0\\y=2ab;\quad \:a\ne \:0$

hence, the correct option  is (C) 2ab .