‘DIGITAL’ ROOTS 43

their respective roots (B), since a number of interesting points
appear:

 

 

 

 

(A) NUMBERS (B) rooTs
1 gl 8RR S AU U R S
g A B TR TR g D 2 A BB R I B
3 0 QY AR RE e A X8 Rl o 8 .69 g Bl a0
4 -8 12 a6 L oa. i dignd v gt na 4B o s e R
5 - 10 15 20 Lasl a0 i an et g0 BT G B eSS
6 T2 18/ 94" 30/ le6 A8 148 6/ il 56 sk 00609
7 14 21 28 35 42 49 56 T8 8 BB g
8 16 24 32 40 48 56 64 Be0 i O R A
9 18 a7.80 45" 84 .00 S8 0n G9d SFG
10 20 30 40 50 60 70 8o Y o R Gl 8
1T 22> 3974488 B0 SRR E gt W 1 gl B
1224 36 48 1160 72 84 96 31 6090 060 G /9B
13 26 39 52 65 78 91 104 A i A e a b e
1498 49" 86,00 1 84 A Q8 1T BB GG a8
15 30 45 60 75 90 105 120 &8 g Gy 6.8
1632/ 48 164 8o/ ol 1127 128 et kgl T (8 AT
17,2 3A BT A0S D8s LY 0TI gL T ELE 8B R A Y
18 36 54 72 9o 108 126 144 | 9 9 9 9 9 9 9 9

 

 

This table shows quite clearly that the digital roots of all
multiples of g are themselves also 9. They appear in the table
as a row of nines. If the table is ruled at these rows, the
rulings divide the table into two sections, and it will be seen
that in the roots columns, each divided section is identical.

The following facts also appear:

(a) In each roots section, the roots forming the diagonals
of the section are palindromic. One of these diagonals (from
left to right in the first section) represents the square
numbers.

(b) The roots of all square numbers, in order from 1 up-
wards, are 1, 4, 9, 7, 7, 9, 4, I in that order, and this order is
repeated indefinitely. In the same way, although this is not
revealed by the table, the roots of all cube numbers are 1, 8,
9, in that order.

(¢) The root of any multiple of 3 is always 3, 6, or g.

(d) The root of any number not a multiple of 3 is not

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