a$)$ What size of ISO bolt made from SAE class $9\mathrm{.}8$ steel is needed to carry a

static tensile load of $25kN$ with a safety factor of $4$ based on proof strength?

b$)$ If this bolt is used with a nut made of steel corresponding to SAE class $4\mathrm{.}6$

specifications, what is the least number of threads that must be engaged for the

thread shear yield strength to be equal to the bolt tensile yield strength?