The Collaborative International Dictionary
Prime \Prime\, a. [F., fr. L. primus first, a superl. corresponding to the compar. prior former. See Prior, a., Foremost, Former, and cf. Prim, a., Primary, Prince.]

First in order of time; original; primeval; primitive; primary. ``Prime forests.''
Tennyson.She was not the prime cause, but I myself.
Milton.Note: In this sense the word is nearly superseded by primitive, except in the phrase prime cost.
First in rank, degree, dignity, authority, or importance; as, prime minister. ``Prime virtues.''
Dryden.First in excellence; of highest quality; as, prime wheat; a prime quality of cloth.

Early; blooming; being in the first stage. [Poetic]
His starry helm, unbuckled, showed him prime In manhood where youth ended.
Milton. Lecherous; lustful; lewd. [Obs.]
Shak.Marked or distinguished by a mark (') called a prime mark.

(Math.)
Divisible by no number except itself or unity; as, 7 is a prime number.

Having no common factor;  used with to; as, 12 is prime to 25. Prime and ultimate ratio. (Math.). See Ultimate. Prime conductor. (Elec.) See under Conductor. Prime factor (Arith.), a factor which is a prime number. Prime figure (Geom.), a figure which can not be divided into any other figure more simple than itself, as a triangle, a pyramid, etc. Prime meridian (Astron.), the meridian from which longitude is reckoned, as the meridian of Greenwich or Washington. Prime minister, the responsible head of a ministry or executive government; applied particularly to that of England. Prime mover. (Mech.)
A natural agency applied by man to the production of power. Especially: Muscular force; the weight and motion of fluids, as water and air; heat obtained by chemical combination, and applied to produce changes in the volume and pressure of steam, air, or other fluids; and electricity, obtained by chemical action, and applied to produce alternation of magnetic force.
An engine, or machine, the object of which is to receive and modify force and motion as supplied by some natural source, and apply them to drive other machines; as a water wheel, a waterpressure engine, a steam engine, a hotair engine, etc.

Fig.: The original or the most effective force in any undertaking or work; as, Clarkson was the prime mover in English antislavery agitation.
Prime number (Arith.), a number which is exactly divisible by no number except itself or unity, as 5, 7, 11.
Prime vertical (Astron.), the vertical circle which passes through the east and west points of the horizon.
Primevertical dial, a dial in which the shadow is projected on the plane of the prime vertical.
Primevertical transit instrument, a transit instrument the telescope of which revolves in the plane of the prime vertical,  used for observing the transit of stars over this circle.
Wiktionary
n. A factor of a given integer which is also a prime number. vb. (context transitive English) to reduce an integer to its set of prime factors
WordNet
n. the prime factors of a quantity are all of the prime quantities that will exactly divide the given quantity
Wikipedia
In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicities; the process of determining these factors is called integer factorization. The fundamental theorem of arithmetic says that every positive integer has a single unique prime factorization.
To shorten prime factorizations, factors are often expressed in powers (multiplicities). For example,
360 = 2 × 2 × 2 × 3 × 3 × 5 = 2 × 3 × 5,
in which the factors 2, 3 and 5 have multiplicities of 3, 2 and 1, respectively.
For a prime factor p of n, the multiplicity of p is the largest exponent a for which p divides n exactly.
For a positive integer n, the number of prime factors of n and the sum of the prime factors of n (not counting multiplicity) are examples of arithmetic functions of n that are additive but not completely additive.
Usage examples of "prime factor".
He sets aside (for example) a box labeled HARVARDWATERHOUSE PRIME FACTOR CHALLENGE '4952 to reveal a stack of bricks, neatly wrapped in paper that has gone gold with age, each consisting of a short stack of ETC cards, and each labeled ARETHUSA INTERCEPTS with a date from 1944 or '45.
So it is written, so it was done, the Ring placed in Wennn Stogggul's greedy hands in exchange for the SaTrryn becoming Prime Factor.
The Prime Factor is desperate to destroy you because you are the only person standing in his way.
It had been Sornnn SaTrryn's intention to make all haste back to Axis Tyr, there to return to his duties both as Prime Factor and as a de facto member of the Kundalan Resistance.
In this second life I am like an observer of my other self, and I tell you, Prime Factor, that I do not care for what I see.
In modern agriculture oil is the prime factoras power for farm machinery (obviously) but also for insecticides and for fertilizers.
In modern agriculture oil is the prime factor  as power for farm machinery (obviously) but also for insecticides and for fertilizers.
So while he made better and better computers to solve the HarvardWaterhouse Prime Factor Challenge, my friends at the NSA watched him, and learned.
Alcohol is the prime factor in determining the calorie content of beer  the carbohydrate and protein percentages hardly matter at all.
As has been said, Hilton had made it a prime factor of his job to become thoroughly well acquainted with every member of his staff.
And it seems from what has been said that the human Overgovernment must be considered now as a prime factor.
Always, a prime factor in this dream was Gorenko's desire to change his Navy from a homeland defense force to a bluewater fleet, commanding the oceans of the world.