# Factors of Repunits

## Theorem

The decimal representations of the reciprocals of the first few prime numbers are as follows:

$R_n$ Factors of $n$ Also see
$2$ $11$
$3$ $3 \times 37$
$4$ $11 \times 101$
$5$ $41 \times 271$
$6$ $3 \times 7 \times 11 \times 13 \times 37$
$7$ $239 \times 4649$
$8$ $11 \times 73 \times 101 \times 137$
$9$ $3^2 \times 37 \times 333 \, 667$
$10$ $11 \times 41 \times 271 \times 9091$
$11$ $21 \, 649 \times 513 \, 239$
$12$ $3 \times 7 \times 11 \times 13 \times 37 \times 101 \times 9901$
$13$ $53 \times 79 \times 265 a, 371 \, 653$