To find the greatest common factor (GCF) of each pair of monomials, we need to consider both the numerical coefficients and the variable parts separately.
### Pair 1: [tex]\(18x^2y\)[/tex] and [tex]\(16xy\)[/tex]
1. Numerical Coefficients:
- Identify the coefficients: 18 and 16.
- Find the GCF of 18 and 16. The GCF of 18 and 16 is 2.
2. Variable Parts:
- Identify the variables in both monomials: [tex]\(x^2y\)[/tex] and [tex]\(xy\)[/tex].
- For [tex]\(x\)[/tex]:
- The smallest power of [tex]\(x\)[/tex] in both variables is [tex]\(x\)[/tex].
- For [tex]\(y\)[/tex]:
- The smallest power of [tex]\(y\)[/tex] in both variables is [tex]\(y\)[/tex].
Combining these, the GCF of the monomials [tex]\(18x^2y\)[/tex] and [tex]\(16xy\)[/tex] is [tex]\(2xy\)[/tex].
### Pair 2: [tex]\(28ab^3\)[/tex] and [tex]\(10a^2b^2\)[/tex]
1. Numerical Coefficients:
- Identify the coefficients: 28 and 10.
- Find the GCF of 28 and 10. The GCF of 28 and 10 is 2.
2. Variable Parts:
- Identify the variables in both monomials: [tex]\(ab^3\)[/tex] and [tex]\(a^2b^2\)[/tex].
- For [tex]\(a\)[/tex]:
- The smallest power of [tex]\(a\)[/tex] in both variables is [tex]\(a\)[/tex].
- For [tex]\(b\)[/tex]:
- The smallest power of [tex]\(b\)[/tex] in both variables is [tex]\(b^2\)[/tex].
Combining these, the GCF of the monomials [tex]\(28ab^3\)[/tex] and [tex]\(10a^2b^2\)[/tex] is [tex]\(2ab^2\)[/tex].
### Summary
From the above steps, the GCFs of the given monomial pairs are:
1. The GCF of [tex]\(18x^2y\)[/tex] and [tex]\(16xy\)[/tex] is [tex]\(2xy\)[/tex].
2. The GCF of [tex]\(28ab^3\)[/tex] and [tex]\(10a^2b^2\)[/tex] is [tex]\(2ab^2\)[/tex].
Therefore, the full answer is:
- For [tex]\(18x^2y\)[/tex] and [tex]\(16xy\)[/tex], the GCF is [tex]\(2xy\)[/tex].
- For [tex]\(28ab^3\)[/tex] and [tex]\(10a^2b^2\)[/tex], the GCF is [tex]\(2ab^2\)[/tex].
