Question

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

Answer 1

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

Answer 2

Greatest common factor of
`15x^2y^3` and
`-18x^3yz` is
`3x^2y`

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 * 5 * x* x * y * y * y`

and Similarly,
`-18x^3yz` can be written as,

`-18x^3yz=-3 * 3* 2 * x* x * x* y* z`

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

Greatest common factor as
`3x^2y`