Greatest common divisors can in principle be computed by determining the prime factorizations of the two numbers and comparing factors, as in the following example: to compute gcd ( 18, 84 ), we find the prime factorizations 18 = 2 · 3 < sup > 2 </ sup > and 84 = 2 < sup > 2 </ sup > · 3 · 7 and notice that the " overlap " of the two expressions is 2 · 3 ; so gcd ( 18, 84 ) = 6.

: This formula is often used to compute least common multiples: one first computes the gcd with Euclid's algorithm and then divides the product of the given numbers by their gcd.

Because gcd ( a, b ) is a divisor of both a and b, it's more efficient to compute the LCM by dividing before multiplying:

* gcd ( m, n ) × lcm ( m, n ) = m × n. Finding the prime factors is often harder than to compute gcd and lcm with other algorithms which do not require known prime factorization.

It will consist of 48 racks ( 49, 152 compute nodes ), with 70 PB of disk storage ( 470 GB / s I / O bandwidth ).

It was used to compute the first 206, 158, 430, 000 decimal digits of π on September 18 to 20, 1999, and the results were checked with Borwein's algorithm.

An account of small cash sums received over a few days at the fort of Vindolanda circa 110 AD shows that the fort could compute revenues in cash on a daily basis, perhaps from sales of surplus supplies or goods manufactured in the camp, items dispensed to slaves such as cervesa ( beer ) and clavi caligares ( nails for boots ), as well as commodities bought by individual soldiers.

This number can be seen as equal to the one of the first definition, independently of any of the formulas below to compute it: if in each of the n factors of the power one temporarily labels the term X with an index i ( running from 1 to n ), then each subset of k indices gives after expansion a contribution X < sup > k </ sup >, and the coefficient of that monomial in the result will be the number of such subsets.

To compute the derivative of 1 / g ( x ), notice that it is the composite of g with the reciprocal function, that is, the function that sends x to 1 / x.

A common solution is to compute a fixed hash function with a very large range ( say, 0 to 2 < sup > 32 </ sup > − 1 ), divide the result by n, and use the division's remainder.

To compute dust and smoke impacts, they employed a one-dimensional microphysics / radiative-transfer model of the Earth's lower atmosphere ( to the mesopause ), which defined only the vertical characteristics of the global climate perturbation.

Like the " dimension of image " characterization this can be generalized to a definition of the rank of a linear map: the rank of a linear map f from V → W is the minimal dimension k of an intermediate space X such that f can be written as the composition of a map V → X and a map X → W. While this definition does not suggest an efficient manner to compute the rank ( for which it is better to use one of the alternative definitions ), it does allow to easily understand many of the properties of the rank, for instance that the rank of the transpose of A is the same as that of A.

Thinking of matrices as tensors, the tensor rank generalizes to arbitrary tensors ; note that for tensors of order greater than 2 ( matrices are order 2 tensors ), rank is very hard to compute, unlike for matrices.

This fact, combined with the fact that some elements almost always have certain oxidation states ( due to their very high electropositivity or electronegativity ), allows one to compute the oxidation states for the remaining atoms ( such as transition metals ) in simple compounds.

When the distribution follows a log-normal curve ( values expressed in decibels ), the mean and standard deviation can be used to compute the medium-power talker.

Bayes ' theorem was named after the Reverend Thomas Bayes ( 1702 – 61 ), who studied how to compute a distribution for the probability parameter of a binomial distribution ( in modern terminology ).

By communicating to each other one bit at a time ( adopting some communication protocol ), Alice and Bob want to compute the value of such that at least one party knows the value at the end of the communication.

This sequence can be used to approximate the distribution ( i. e., to generate a histogram ), or to compute an integral ( such as an expected value ).

The so-called " 3M computer " had a Megabyte of memory, a Megapixel display ( roughly 1000x1000 ), and a " MegaFLOPS " compute performance ( at least one million floating point operations per second ).

In complex analysis, a field in mathematics, the residue theorem, sometimes called Cauchy's residue theorem ( one of many things named after Augustin-Louis Cauchy ), is a powerful tool to evaluate line integrals of analytic functions over closed curves ; it can often be used to compute real integrals as well.

Each Blue Gene / L node was attached to three parallel communications networks: a 3D toroidal network for peer-to-peer communication between compute nodes, a collective network for collective communication ( broadcasts and reduce operations ), and a global interrupt network for fast barriers.

" Connectance ( C ) is the fraction of all possible links that are realized ( L / S < sup > 2 </ sup >) and represents a standard measure of food web complexity ..." The distance ( d ) between every species pair in a web is averaged to compute the mean distance between all nodes in a web ( D ) and multiplied by the total number of links ( L ) to obtain link-density ( LD ), which is influenced by scale dependent variables such as species richness.

Most of the available algorithms to compute pi ( π ), on the other hand, cannot be easily split up into parallel portions.

Say, to get B! P, first compute 2P, then 3 ( 2P ), then 4 ( 3! P ), and so on.

Given this s, we can compute the coordinates of 2 ( 2P ), just as we did above: 4P =( 259851, 116255 ).

Weights are easy to calculate as well: a standard A4 sheet made from 80 gram / m paper weighs 5 grams ( as it is one 16th of an A0 page, measuring 1 m ), allowing one to easily compute the weight — and associated postage rate — by counting the number of sheets used.

The Cayley – Hamilton theorem always provides a relationship between the powers of A ( though not always the simplest one ), which allows one to simplify expressions involving such powers, and evaluate them without having to compute the power A < sup > n </ sup > or any higher powers of A.

This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.

Another divide and conquer algorithm with a single subproblem is the Euclidean algorithm to compute the greatest common divisor of two numbers ( by reducing the numbers to smaller and smaller equivalent subproblems ), which dates to several centuries BC.

For example, if you have the unit thermal resistance of a wall, divide by the cross-sectional area of the depth of the wall to compute the thermal resistance.

To compute the number of states we must compute the volume in phase space in which the system can be found and divide that by.

The idea behind it is, to divide the set of N samples into L sets of M samples, compute the DFT of each set, square it to get the power spectral density and compute the average of all of them.

To compute this figure, take the stock price and divide it by the annual EPS figure.

To compute the PEG ratio, divide the Forward P / E by the expected earnings growth rate ( you can also use historical P / E and historical growth rate to see where it's traded in the past ).

To compute the ratio, take the pro forma net income ( same one used in the EPS figure mentioned above ) and divide it by the invested capital.

To compute it, divide the EV by the net sales for the last four quarters.

To compute, divide the EV by EBITDA ( see above for calculations ).

So, unlike it may be seen by modern reader, his goal was not to use moves of counters on a board to multiply, divide and find square roots, but rather to find a way to compute symbolically, as we learned to do it at school up to a few decade ago.

Take any Lorentzian manifold, compute its Einstein tensor, which is a purely mathematical operation, divide by, and declare the resulting symmetric second rank tensor field to be the stress-energy tensor.

To compute the P / E ratio for the case of a rented house, divide the price of the house by its potential earnings or net income, which is the market annual rent of the house minus expenses, which include maintenance and property taxes.

Kepler could divide up the orbit into an arbitrary number of parts, compute the planet's position for each one of these, and then refer all questions to a table, but he could not determine the position of the planet at each and every individual moment because the speed of the planet was always changing.