Quadrillion

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This article is about the short scale quadrillion. For details about differing meanings of the word, see long and short scales.

One quadrillion, 10^15, 1,000,000,000,000,000 is a large number that comes after trillion. In the long scale, this number is refer to as a billiard.

Quadrillion is the lowest natural number with a "q" in its name. A quadrillion has 255 proper divisors. The divisor function calculated on a quadrillion is equal to:

[ \sigma(10^)\;=\;2,499,961,853,010,960]

and therefore its abundancy is 499,961,853,010,960, which is almost half of a quadrillion. The divisor function of a quadrillion (and indeed, of all high powers of ten) may be calculated with the formula:

[ \sigma(10^n)\;=\;\frac - 1)(5^ - 1)}]

which may be seen by applying the formula for the partial sum of a geometric series twice to the sum of the divisors.

Quadrillion

See also