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Verified Answer :

the GCF is 3m^2n <===

Answer:

\(3m^2n\)

Step-by-step explanation:

Since,

\(48m^5n=3\times 2\times 2\times 2\times 2\times m\times m\times m\times m\times m\times n\)

\(81m^2n^2=3\times 3 \times 3\times 3\times m\times m\times n\times n\)

Thus,

\(\text{GCF of }48m^5n\text{ and }81m^2n^2=3\times m\times m\times n\)

\(=3m^2n\)