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#### Finding The Remainder When n_{b} Is Divided By (b-1):

A. When a
number in base 10 is divided by 9, you add up all the digits and find the
remainder of the sum. The same applies for any base when it is divided by
the base minus 1.

B.
Examples:

Ex [1]
143243_{5} ÷ 4 has a remainder of _____

a.
1+4+3+2+4+3 = 17 which has a remainder of 1 when divided by 4.

b. The
answer is 1.

c. Note: you
do not have to add all the numbers. We know 4 is divisible by 4, so you
can add 1+3+2+3 = 9.

Ex [2]
173763_{8} ÷ 7 has a remainder of ______

a. Ignoring
7, we get 1+3+6+3 = 13 which has a remainder of 6 when divided by 7.

b. The
answer is 6.

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