# Divisor Sentence Examples

- Greatest Common
**Divisor**3.4.3 47. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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 we resolve two numbers into their prime factors, we can find their Greatest Common
**Divisor**or Highest Common Factor (written G.C.D. - (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 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. - In determining the rate of a " dividend "), approximate expression of the
**divisor**in terms of the largest unit is sufficient. - If n is a
**divisor**of N,