HH R TR T i et e

6
Di ViSibilit)/

The behaviour of digits as members of a number, either
singly or in groups, is most enlightening when it is necessary
to ascertain, without actually dividing out, whether a cer-
tain number is exactly divisible by a specified divisor. Tests
of divisibility are readily available where the divisor is rela-
tively small, and they are easily explained:

Divisor 1 All numbers are divisible by 1.

Divisor 2 Every number is a multiple of 10, plus its unit
digit. Every multiple of 10 is divisible by 2, so
that if the last digit of a number is divisible by 2,
then so is the number itself.

Divisor 3 A number is divisible by g if its digital root is
divisible by g. To prove this, it should be noted

that:

: TR b s that is, in each case, we have a
100=99+1r Iultiple of g, plus 1
1I0= Q-1 ¥ » P .
1 Similarly:
5000 =multiple of g, plus 5
f 400 = 3 ” » 4
; 20= » » » 2

So that:

5420=multiple of 3, +(2+4-+5)
As, therefore, 2 445 is not divisible by 3, then
also 5420 is not.
64

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