The H.C.F. is given
[tex]\begin{aligned} \rm H.C.F.(4,16) &= H.C.F.( 1, 4 )\\H.C.F.(20, 65) &= H.C.F.( 1, 5 )\\H.C.F.(2x, 4) &= H.C.F.( 1, 2)\\H.C.F.(14xy, 42x) &= H.C.F.( 1,14,x)\\\end{aligned}[/tex]
It means the highest common factor.
[tex]\begin{aligned} \rm H.C.F.(4,16) &= H.C.F.( 1*4,\ 1*4*4 ) = H.C.F.( 1, 4 )\\H.C.F.(20, 65) &= H.C.F.( 1*4*5,\ 1*5*13 ) = H.C.F.( 1, 5 )\\H.C.F.(2x, 4) &= H.C.F.( 1*2*x,\ 1*2*2 ) = H.C.F.( 1, 2)\\H.C.F.(14xy, 42x) &= H.C.F.(1*14*x*y,\ 1*14*3*x) = H.C.F.( 1,14,x)\\\end{aligned}[/tex]
Thus, the H.C.F. is given
[tex]\begin{aligned} \rm H.C.F.(4,16) &= H.C.F.( 1, 4 )\\H.C.F.(20, 65) &= H.C.F.( 1, 5 )\\H.C.F.(2x, 4) &= H.C.F.( 1, 2)\\H.C.F.(14xy, 42x) &= H.C.F.( 1,14,x)\\\end{aligned}[/tex]
More about the H.C.F. link is given below.
https://brainly.com/question/120215
