Answer :

[tex]16|2\\.\ 8|2\\.\ 4|2\\.\ 2|2\\.\ 1|\\16=\fbox2\cdot\fbox2\cdot\fbox2\cdot\fbox2\\\\48|2\\24|2\\12|2\\.\ 6|2\\.\ 3|3\\.\ 1|\\48=\fbox2\cdot\fbox2\cdot\fbox2\cdot\fbox2\cdot3[/tex]

[tex]therefore\ GCF(16;\ 48)=\fbox2\cdot\fbox2\cdot\fbox2\cdot\fbox2=\boxed{\boxed{16}}[/tex]

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