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quadrillion
The quadrillion is a large number which has one of two values depending on how or where it is being used. Quadrillion comes after trillion.
Short scale usage
In short scale usage, a quadrillion is equal to a 1 with 15 zeroes, namely: 1,000,000,000,000,000 (1015)
It is a thousand trillion (short scale), i.e. a thousand million million. The SI prefix for this number is peta.
Long scale usage
In long scale usage, a quadrillion is equal to a 1 with 24 zeroes, namely: 1,000,000,000,000,000,000,000,000 (1024)
It is a thousand sextillion (short scale), The SI prefix for this number is yotta.
While people in the British Isles, Australia and New Zealand traditionally employed the long scale usage, they have largely switched to the short scale usage.
Properties
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:
- <math> \sigma(10^{15})\;=\;2,499,961,853,010,960</math>
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:
- <math> \sigma(10^n)\;=\;\frac{(2^{n+1} - 1)(5^{n+1} - 1)}{4}</math>
which may be seen by applying the formula for the partial sum of a geometric series twice to the sum of the divisors.
