Greatest Common Divisor 3.4.3 47.
Applications of simple continued fractions to the theory of numbers, as, for example, to prove the theorem that a divisor of the sum of two squares is itself the sum of two squares, may be found in J.
(iv.) In algebra we have a theory of highest common factor and lowest common multiple, but it is different from the arithmetical theory of greatest common divisor and least common multiple.
If n is a divisor of N,
Algebraical division therefore has no definite meaning unless dividend and divisor are rational integral functions of some expression such as x which we regard as the root of the notation (ï¿½ 28 (iv.)), and are arranged in descending or ascending powers of x.
In long division the divisor is put on the left of the dividend, and the quotient on the right; and each partial product, with the remainder after its subtraction, is shown in full.
If we resolve two numbers into their prime factors, we can find their Greatest Common Divisor or Highest Common Factor (written G.C.D.
So far as the resultant velocity ratio is concerned, the order of the drivers N and of the followers n is immaterial: but to secure equable wear of the teeth, as explained in 44, the wheels ought to be so arranged that, for each elementary combination, the greatest common divisor of N and ii shall be either 1, or as small as possible.
If the greatest common divisor of N and n be d, a number less than n, so that n=md, N~Md; then a=mN=Mn=Mmd; b=M; c=m.
They there fore study that the numbers of teeth in each pair of wheels whici work together shall either be prime to each other, or shall hav their greatest common divisor as small as is consistent with velocity ratio suited for the purposes of the machine.
Division by a Mixed Number.-To divide by a mixed number, when the quotient is seen to be large, it usually saves time to express the divisor as either a simple fraction or a decimal of a unit of one of the denominations.
In short division the divisor and the quotient are placed respectively on the left of and below the dividend, and the partial products and remainders are not shown at all.
The term division is therefore used in text-books to describe the two processes described in §§ 38 and 39; the product mentioned in § 34 is the dividend, the number or the unit, whichever is given, is called the divisor, and the unit or number which is to be found is called the quotient.
Methods of Division.-What are described as different methods of division (by a single divisor) are mainly different methods of writing the successive figures occurring in the process.
in determining the rate of a " dividend "), approximate expression of the divisor in terms of the largest unit is sufficient.
divisor definition has the best brevity.
Then 3 does not divide n; each prime divisor of n divides m.
Here det must be an integer which is a multiple of the biggest determinant divisor of A.
divisor length of n.
divisor problem in general.
An ordinary formula for obtaining it is 1 S for highpressure engines, and S for condensing engines, where D is the diameter of the piston in inches and S the length of the stroke in feet, though varying numbers are used for the divisor.
divisor of n divides m.
divisor of two integers.
divisor of these polynomials.
It is used to find the greatest common divisor, or highest common factor, of two given numbers.
We say that integers a and b have a common divisor c if c is a divisor if both a and b.
To calculate the greatest common divisor of two integers and of two polynomials over a field.
As we keep lowering the divisor, more parties will get seats, more seats will be awarded.
An upper bound d for the highest power of p appearing in an elementary divisor of A must be given.
Gockel (37) says that the results he obtained without the cover when divided by 3 are fairly comparable with those obtained under the usual conditions; but the appropriate divisor must vary to some extent with the climatic conditions.
It will be noticed that the rods only give the multiples of the number which is to be multiplied, or of the divisor when they are used for division, and it is evident that they would be of little use to any one who knew the multiplication table as far as 9 X9.
In multiplications or divisions of any length it is generally convenient to begin by forming a table of the first nine multiples of the multiplicand or divisor, and Napier's bones at best merely provide such a table, and in an incomplete form, for the additions of the two figures in the same parallelogram have to be performed each time the rods are used.
(ii.) The elements of the theory of numbers belong to arithmetic. In particular, the theorem that if n is a factor of a and of b it is also a factor of pa= qb, where p and q are any integers, is important in reference to the determination of greatest common divisor and to the elementary treatment of continued fractions.
Moreover, if the last divisor is uL, then it follows from the theory of numbers (Ã¯¿½ 26 (ii.)) that (a) u is a factor of p and of q, and (b) any number which is a factor of p and q is also a factor of u.
Algebraical division therefore has no definite meaning unless dividend and divisor are rational integral functions of some expression such as x which we regard as the root of the notation (Ã¯¿½ 28 (iv.)), and are arranged in descending or ascending powers of x.
The deficiencies of the Greek symbolism were partially remedied; subtraction was denoted by placing a dot over the subtrahend; multiplication, by placing bha (an abbreviation of bhavita, the product ") after the factors; division, by placing the divisor under the dividend; and square root, by inserting ka (an abbreviation of karana, irrational) before the quantity.
Division was accomplished by multiplying the divisor until the dividend was reached; the answer being the number of times the divisor was so multi- I plied.
The original dividend is written as 0987063, since its initial figures are greater than those of the divisor; if the dividend had commenced with (e.g.) 3.
Division.-In the same way, in performing approximate division, we can at a certain stage begin to abbreviate the divisor, taking off one figure (but with correction of the final figure of the partial product) at each stage.
Look at your IRA balance from Dec. 31 of last year, divide it by the proper divisor shown in Appendix C of IRS Publication 590 Individual Retirement Arrangements, and withdraw at least that amount by Dec. 31.
RMD - Use your IRA balance from Dec. 31 of the year before last year, your age at the end of last year, and the proper divisor in Appendix C of IRS Publication 590.
RMD - Take your IRA balance from Dec. 31 of last year and divide it by the proper divisor in Appendix C of IRS Publication 590.
The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.