Answer: The correct option is (A) 13xy.
Step-by-step explanation: We are given to select the greatest common factor (G.C.F) of the following two expressions :
[tex]91x^2y~~~~\textup{and}~~~~104xy^3.[/tex]
The G.C.F. of two numbers is the product of the common terms in the prime factorization of the expressions.
We have
[tex]91x^2y=7\times 13\times x\times x\times y,\\\\104xy^3=2\times2\times2\times13\times x\times y\times y\times y.[/tex]
Therefore, the G.C.F. of the given expressions will be
[tex]G.C.F.=13\times x\times y=13xy.[/tex]
Thus, the required G.C.F is 13xy.
Option (A) is CORRECT.
