# Why did the ancient Greek count 1 in case of perfect numbers but not otherwise

In the mathematics of the ancient Greek 1 has not been considered to be a number. Nevertheless 1 counted as a divisor of perfect numbers like 6 = 1 + 2 + 3. Is there any explanation for this inconsistency?

• Why do you think that 1 was not considered a number by Greeks, is there a source? Greeks had a numeral for it since the time immemorial, and Pythagoreans distinguished it as "the number of reason" in their numerology. Commented Oct 28, 2016 at 21:41
• @Conifold: Euclid excludes 1 as a number. Commented Oct 29, 2016 at 7:32
• @Conifold. I think you are confusing "numerals" and "numbers".
– fdb
Commented Oct 29, 2016 at 11:07
• I suspect that Euclid was influenced (through Plato) by the refined Parmenidian concerns that multiplicity and change are illusions and only One is (he strives to keep motion out of geometric arguments for similar reasons). But it had little effect on common usage by Greeks, or even mathematical usage, Euclid himself does not maintain the distinction consistently in the Elements. Commented Oct 30, 2016 at 21:20
• The Treviso arithmetic of 1453 also excludes 1as a number. Commented Nov 13, 2016 at 4:23