Gnpth wrote:
What is the Greatest Common Factor (GCF) of \(18x^8y^{(20)}\) and \(24x^{(12)}y^{(15)}\)?
A. \(3x^4y^5\)
B. \(6x^4y^5\)
C. \(3x^8y^{(15)}\)
D. \(6x^8y^{(15)}\)
E. \(72x^{(12)}y^{(20)}\)
To find GCF, find the prime factorization of both expressions.
\(18x^8y^{(20)}\) =
\(2 * 3 * 3 * x^8 * y^{(20)}\)
\(24x^{(12)}y^{(15)}\) =
\(2 * 2 * 2 * 3 * x^{(12)} * y^{(15)}\)
Find all the factors they have in common, "to the lowest power."
Both expressions have 2 as a factor, for example, but the second expression has two more copies of 2. The first expression has only one copy of 2. Only one copy of 2 -- i.e., only one power of 2 -- can be counted towards the GCF.
For variables raised to powers, the lower power is the limiting factor used to find GCF.
Factors in common:
\(2 * 3 * x^8 * y^{(15)} =\)
\(6x^8y^{(15)}\)
Answer D
_________________
SC Butler has resumed!Get
two SC questions to practice, whose links you can find by date,
here.Tell me, what is it you plan to do with your one wild and precious life? --
Mary Oliver