Final answer:
The greatest common factor (GCF) of the expressions 91x²y and 104xy³ is 13xy, as both numbers are divisible by 13 and each expression contains at least one factor of both x and y.
Step-by-step explanation:
The student is asking for the Greatest Common Factor (GCF) of two algebraic expressions, 91x²y and 104xy³. To find the GCF, we look for the highest power of each common factor in both terms. In this instance, the common factors are the variables x, y, and the number 13, since 91 and 104 are both divisible by 13.
Both terms have at least one x, so x is part of the GCF. They also both have at least one y, so y is also part of the GCF. Since 91 = 13 × 7 and 104 = 13 × 8, and 13 is the only common numerical factor, it is included in the GCF. Therefore, the GCF is 13xy.