Question

Question 2 (5 points)
Find the greatest common factor of 48xy3z, 24x2y3z, and 56x2yz.
A) 16xyz
B) 8xyz
C) 8xyz
D) XyZ

Answers

  1. Answer:

    The greatest common factor is 8xyz

    Step-by-step explanation:

    To find the greatest common factor of an expression involving numbers and variables, we find each greatest common factor separately.

    Numbers:

    48, 24 and 56.

    We find the greatest common factor factoring them simultaneously while all can be factored by the same number. The GCF is the multiplication of the factors. So

    48 – 24 – 56|2

    24 – 12 – 28|2

    12 – 6 – 14|2

    6 – 3 – 7|

    They cant be factored by the same factors anymore, so the numeric GCF is 8.

    Variables:

    For each variable, the GCF will be the lowest exponent.

    Variable x: We have exponents 1, 2 and 2. So the GCF is x^1 = x

    Variable y: We have exponents 3, 3 and 1. So the GCF is y^1 = y

    Variable z: We have exponents 1, 1 and 1. So the GCF is z^1 = z

    The greatest common factor is:

    8*x*y*z = 8xyz

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