$1)$ An M$20-0\mathrm{.}6$ screw $($material has $\backslash (\backslash$mathrm$\{$E$\}=200\backslash$mathrm$\{$GPa$\}\backslash ))$ with $20-$mm equivalent under$-$head diameter is torqued to $\backslash (100\backslash$mathrm$\{$~N$\}-\backslash$mathrm$\{$m$\}\backslash )$; the fastener has an engaged length of $63$ mm $.$ Assume a friction coefficient of $0\mathrm{.}1$

a$.$ Estimate the clamping load $(4$ points$).$

b$.$ Calculate the nut factor for this scenario $(4$ points$).$