It remains, then, to find how many times 468 contains 18. Proceed exactly as before. Observe that 46 contains 18 more than twice, and less than 3 times; therefore, 460 contains it more than 20, and less than 30 times (77); as does also 468. Subtract 18 20 times from 468, that is, subtract 360; the remainder is 108. Therefore, 468 contains 18 20 times, and as many more as 108 contains it. Now, 108 is found to contain 18 6 times exactly; therefore, 468 contains it 20 + 6 times, and 4068 contains it 200 + 20 + 6 times, or 226 times. If we write down the process that has been followed, without any explanation, putting the divisor, dividend, and quotient, in a line separated by parentheses it will stand, as in example(A). Let it be required to divide 36326599 by 1342 (B). A. B. 18)4068(200 + 20 + 6 1342)36326599(20000 + 7000 + 60 + 9 3600 26840000 ---- -------- 468 9486599 360 9394000 --- ------- 108 92599 108 80520 --- ----- 0 12079 12078 ----- 1 As in the previous example, 36326599 is separated into 36320000 and 6599; the first four figures 3632 being separated from the rest, because it takes four figures from the left of the dividend to make a number which is greater than the divisor. Again, 36320000 is found to contain 1342 more than 20000, and less than 30000 times; and 1342 × 20000 is subtracted from the dividend, after which the remainder is 9486599. The same operation is repeated again and again, and the result is found to be, that there is a quotient 20000 + 7000 + 60 + 9, or 27069, and a remainder 1. Before you proceed, you should now repeat the foregoing article at length in the solution of the following questions. What are 10093874 66779922 2718218 -------- , -------- , ------- ? 3207 114433 13352 the quotients of which are 3147, 583, 203; and the remainders 1445, 65483, 7762.