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104 THE FASCINATION OF NUMBERS

last digit of the cycle must be such as will, when multiplied
by 7, give a number of two digits the second digit of which
must be 9. The only number which satisfies this requirement

 

Derivative
of &= '01408450704225352112676056338028169 | Multiple
Split into 140845 I
groups: 281690 2
422535 3
563380 4
704225 5
845070 6
1126760 8
1267605 9
1408450 10
1690140 12
2112676 15
2253521 16
2535211 18
2676056 19
3380281 24
3521126 25
3802816 27
4084507 29
4507042 32
5211267 37
5352112 38
5070422 36
6338028 45
6760563 48
9014084 64
6056338 43
6901408 49
7605633 54
8028169 5%
8169014 58

 

 

is 49 (=7 X7) and the last digit of the cycle must therefore
be7.

But the digit 4 in the number 49 is a remainder from a
previous division in which another digit g has been ‘brought
down’. As the remainder from g is 4, it follows that the next
to the last digit in the cycle must be such that, when multi-