Prime factorization

Common alloying elements include nickel to improve low temperature mechanical properties chromium, molybdenum, and vanadium to improve elevated-temperature properties and silicon to improve properties at ordinary temperatures. Low alloy steels ate not used where corrosion is a prime factor and are usually considered separately from stainless steels. 

Oxygen is a prime factor in the corrosion of system materials and the release, activation, and redeposition of activated corrosion products. 

Centerline-Mounted Pefmey Pump. For refinery appHcations, temperatures, pipe loads, and product flammabiUty are the prime factors ia selecting a pump. 

Capacity requirement is a prime factor in conveyor selection. Belt conveyors, which can be manufac tured in relatively large sizes to operate at high speeds, deliver large tonnages economically. On the other hand, screw conveyors become extremely cumbersome as they get larger and cannot be operated at high speeds without creating serious abrasion problems. 

Pasquill defined six stabihty classes ranging from highly stable, low-turbulence Class F, to unstable, highly turbulent Class A, and he identified the surfece wind speed, intensity of solar radiation, and nighttime sky cover as being the prime factors controlling atmospheric stabihty. PasquiU then correlated observations of the behavior of plumes in terms of their dispersion with the... 

The hardness of an enamel surface is an important property for such items as enamelled sink units, domestic appliances, washing machine tubs which have to withstand the abrasive action of buttons, etc. On Moh s scale most enamels have a hardness of up to 6 (orthoclase). There are two types of hardness of importance to users of enamel, viz. surface and subsurface. The former is more important for domestic uses when one considers the scratching action of cutlery, pans, etc. whereas subsurface hardness is the prime factor in prolonging the life of enamelled scoops, buckets, etc. in such applications as elevators or conveyors of coal and other minerals. 

The prime factorization theorem states that any polynomial f x) can be written in the following form ... 

It is easy to show that every polynomial f x) (not divisible by x) over a finite field J g is a factor of 1—cc , for some power n . The order (sometimes also called the period or exponent) of f x), denoted by ord(/), is the least such n . If f x) = p x) is an irreducible polynomial (other than x) with d[f] = n then ord(/) must divide pTi i There are two important theorems concerning the orders of prime factors and products of relatively prime polynomials over Fg ... 

For a long time, this finding was correlated with the observation that substituents at a radical center tend to enhance its stability (Section 1.1.2). This in turn led to the belief that the degree of stabilization conferred on the product radical by the substituents was the prime factor determining the orientation and rate of radical addition to olefins. That steric, polar, or other factors might favor the same outcome was either considered to be of secondary importance or simply ignored. ... 

There are five prime factors that determine the properties of starches 1. starch is a polymer of glucose (dextrose) 2. the starch polymer is of two types linear and branched 3 the linear polymeric molecules can associate with each other giving insolubility in water 4. the polymeric molecules are organized and packed into granules which are insoluble in water and 5 disruption of the granule structure is required to render the starch polymer dispersible in water. The modification of starch takes into account these factors. 

Oxalate is found to be a frequent impurity in pharmaceutical substances belonging to the category of either organic acids e.g.. anhydrous citric acid, tartaric acid or salts of organic acids e.g., ferrous gluconate, sodium citrate, potassium citrate and sodium cromoglycate. The presence of this impurity is due to the following two prime factors, namely ... 

THE FUNDAMENTAL THEOREM OF ARITHMETIC states that every whole number greater than 1 is the product of prime factors. Furthermore, these prime factors are unique, and there is exactly one set of prime factors. 

Because any number can be broken down into prime factors in exacdy one unique way, you can use this fact to find the GCF and the LCM quickly, using these prime factors. It is helpful to use a tree diagram to find the prime factorization. 

Find the prime factorization of 72. Circle all prime factors. 

Notice that even though two factor trees are illustrated, the resultant set of prime factors is the same. The prime factorization of 72 is 2x2x2x3x3. 

To find the greatest common factor of 72 and 24, list the prime factorizations of each number and then pair up common prime factors. Multiply these common prime factors ... 

Pair up the common prime factors. Multiply them together for the greatest common factor. Now, multiply the GCF with all of the impaired primes left over to find the least common multiple ... 

To find the prime factorization of a number, use a factor tree. 

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