DIVISIBILITY 65

Divisor 4 Every number is a multiple of 100 plus its tens and
units digits. Every multiple of 100 is divisible
by 4, so that if the last two digits of a number
when taken together are also divisible by 4,
then so is the original number.

Duvisor 5 If the last digit of a number is o or 5, then it must
be divisible by 5, for every number is a multiple
of 10, plus its unit digit, and 1o is divisible by 5.

Divisor 6 A number is divisible by 6 if (a) it is even, and (5)
its digital root is divisible by g. The reasons are
of course the same as are shown for the divisors
2 and 3 respectively.

Divisor 7 This is considered with Divisor 13.

Divisor 8 Every number is a multiple of 1000, plus its last
three digits. 1000 is a multiple of 8, so that if
the last three digits taken together are divisible
by 8, then so is the whole number.

Divisor 9 A number is divisible by g if its digital root is
divisible by g, for the same reason as shown for
Divisor 3.

Divisor 1o By definition, any number ending in nought is
made up solely of multiples of 10 without the
addition of any units, whence any number
having o as its last digit must be divisible by 10.

Duvisor 11 A number is divisible by 11 if the totals of alter-
nate digits give a multiple of 11 or o when one
is subtracted from the other. To prove this, it is
to be noted that:

10,000 —1=9,999
1,000+1I= QQO-II

100—I= Q9

1I04+1= II

AR

y

)

R

AR SRS R A R

T

IR

oo

-
&
B
=
ES
i
et
¥
i
13