If possible, find

(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)