Find the GCF (greatest common factor) of the following terms.
{18xy^2, 54xy, 90}
To find the greatest common factor (GCF) of the given terms {18xy^2, 54xy, 90}, we should identify the common factors in the numerical coefficients as well as any common variables.
1. Finding the GCF of numerical coefficients:
The numerical coefficients are 18, 54, and 90.
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54
The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The common factors are 1, 2, 3, 6, 9, and 18.
The greatest common factor of the numerical coefficients is 18.
2. Finding the common variables:
The terms contain the variables x and y. We take the lowest exponent of x and y in the terms.
For x, the lowest exponent in the given terms is 1 (since 54xy has the variable x to the first power).
For y, the lowest power is y^1 (as the term 54xy contains y to the first power and 90 has no y, so we don't consider y for the last term).
Combining the numerical coefficient GCF and the variable parts with the smallest powers:
The GCF for {18xy^2, 54xy, 90} is 18xy.