Verified Answer :

Multiply the GCF of the numerical part 3 and the GCF of the variable part x^2y to get
3x^2y.

Answer:

Greatest common factor of  \(15x^2y^3\) and \(-18x^3yz\) is  \(3x^2y\)

Step-by-step explanation:

Greatest common factor is the common factor for two or more numbers such that greatest common factor divides both the number.

We find  Greatest common factor by

  • doing prime factorization and then
  • taking common factors from all the factors and
  • if they do not have nay term common then  Greatest common factor is 1.

Given Numbers are \(15x^2y^3\) and \(-18x^3yz\)

First we do prime factorization of \(15x^2y^3\).

15 can be written as product of prime 3 and 5, so

\(15x^2y^3=3 \times 5 \times x\times x \times y \times y \times y\)

and Similarly, \(-18x^3yz\) can be written as,

\(-18x^3yz=-3 \times 3\times 2 \times x\times x \times x\times y\times z\)

Thus, taking common from both the terms,we get,

Greatest common factor as \(3x^2y\)


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