Answer :

(a)


(x100)


Prime factorization of 100 = 2x2x5x5 = 22 x 52


The hook-up is (x22) and (x52)


(b)


(x99)


Prime factorization of 99 = 3x3x11 = 32 x 11


The hook-up is (x32) and (x11)


(c)


(x37)


37 itself is a prime number. A hook-up machine by definition must contain more than one machines. Since the factors of 37 are 1 and 37 and we are forbidden to use (x1) machines, no hook-up is possible.


(d)


(x1111)


Prime factorization of 1111 = 11x101


The hook-up is (x11) and (x101)


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