Determine the quotient and remainder in applying the Division Algorithm to the following:
(a) 31 divided by 4
(b) −1001 divided by 12
(c) −10 001 divided by 137
(a) $31 = 7(4) + 3$. The quotient is 7, and the remainder is 3.
(b) $-1001 = -84(12) + 7$. The quotient is -84, and the remainder is 7.
(c) $-10001 = -73(137) + 0$. The quotient is -73, and the remainder is 0.