DIVISIBILITY 69

to the number of hundreds, plus a remainder also equal to the
number of hundreds.

(x) 100-99=x and a remainder x

SO 500--99=5 » » 5
and 60099 =6 iy 28 6

From this it follows that:
[(x)100+7]+- 99=x and a remainder x4y

SO (500+34)= 99=5 and aremainder 5434 (=39)
Now, 534-—100=5 and a remainder of 34
and 534~ 99=5 and a remainder of 34+5

So that to obtain 534--99, it is possible to divide 534 by 100
and add 5 to the remainder, and for larger numbers, the pro-
cess is continuous.

The number 123456789, in order to be divided by 99,
can now be treated thus. Divide 123 by 100. This gives I
and a remainder of 23. Write the figure 1 in the answer; add
the same number (1) to the remainder (28) and carry 24
forward to the next digit, giving the number 244. Divide by
100. This gives 2 with a remainder of 44. Add 2 to 44 and
carry 46 forward and so on.

Fully worked out, this now gives:

847 /46 69 g, 8y 87

99} X a8 1k 7.8
) 0.9

9
8 (remainder
19-+8=27)

5
4

- O O

 

LR e e e

It will be seen that when we reach the sixth digit in the
original number we have, with the 69 brought forward, the
number 696. This divided by 600 gives g6 remainder. This
added to the digit (6) in the answer gives 102. As this exceeds
99 the procedure here is to deduct g9 from the remainder,
adding 1 to the answer digit and carrying forward a reduced
remainder of 102 —99=3.

The same principle can be applied to many numbers in a

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