## Find the greatest common factor of 15x 2 y 3 and -18x 3 yz.

Question

Find the greatest common factor of 15x 2 y 3 and -18x 3 yz.

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Greatest common factor of [tex]15x^2y^3[/tex] and [tex]-18x^3yz[/tex] is [tex]3x^2y[/tex]

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 [tex]15x^2y^3[/tex] and [tex]-18x^3yz[/tex]

First we do prime factorization of [tex]15x^2y^3[/tex].

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

[tex]15x^2y^3=3 times 5 times xtimes x times y times y times y[/tex]

and Similarly, [tex]-18x^3yz[/tex] can be written as,

[tex]-18x^3yz=-3 times 3times 2 times xtimes x times xtimes ytimes z[/tex]

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

Greatest common factor as [tex]3x^2y[/tex]

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