Here's how it "scales". First column is the number of machines. Second column is the number of times you can divide that number of machines in two equally sized groups:

use Math::BigInt;
use 5.010;
my $line = "+----+------------------------+";
say $line;
printf "| %2d | %22s |\n", 2 * $_,
    Math::BigInt->new(2 * $_)->bfac / (2 * Math::BigInt->new($_)->bfac
+)
    for 1 .. 16;
say $line;
__END__
+----+------------------------+
|  2 |                      1 |
|  4 |                      6 |
|  6 |                     60 |
|  8 |                    840 |
| 10 |                  15120 |
| 12 |                 332640 |
| 14 |                8648640 |
| 16 |              259459200 |
| 18 |             8821612800 |
| 20 |           335221286400 |
| 22 |         14079294028800 |
| 24 |        647647525324800 |
| 26 |      32382376266240000 |
| 28 |    1748648318376960000 |
| 30 |  101421602465863680000 |
| 32 | 6288139352883548160000 |
+----+------------------------+
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