greatest common divisor

Examples of greatest common divisor in the following topics:

• Integer Coefficients and the Rational Zeros Theorem

  • If $a_0$ and $a_n$ are nonzero, then each rational solution $x= \frac {p}{q}$, where $p$ and $q$ are coprime integers (i.e. their greatest common divisor is $1$), satisfies:
  • Since any integer has only a finite number of divisors, the rational root theorem provides us with a finite number of candidates for rational roots.

• Complex Fractions

  • Therefore, we use the cancellation method to simplify the numbers as much as possible, and then we multiply by the simplified reciprocal of the divisor, or denominator, fraction:
  • You'll find that the common denominator of the two fractions in the numerator is 6, and then you can add those two terms together to get a single fraction term in the larger fraction's numerator:

• Terrorism

  • The threat of terrorism is one of the greatest challenges facing the United States and the international community.
  • The threat of terrorism is one of the greatest challenges facing the United States and the international community.
  • Common definitions of terrorism refer to those violent acts that are intended to create fear (terror).

• Simplifying, Multiplying, and Dividing Rational Expressions

  • which, after canceling the common factor of $(x+2)$ from both the numerator and denominator, gives the simplified expression
  • Recall the rule for dividing fractions: the dividend is multiplied by the reciprocal of the divisor.

• Strategy for General Problem Solving

  • Some of the common ones include mass (ton, pounds, ounces, grains, grams); length (yard, feet, inches, meters); and energy (Joule, erg, kcal, eV).
  • The term "conversion factor" is the multiplier, not divisor, which yields the result.

• Introduction to Factoring Polynomials

  • Factoring by grouping divides the terms in a polynomial into groups, which can be factored using the greatest common factor.
  • Factor out the greatest common factor, $4x(x+5) + 3y(x+5)$.

• The stages of going international

  • First, the process tends to be ranked in order of "least risk and investment" to "greatest involvement".
  • Second, these are not necessarily sequential steps, even though exporting is apparently most common as an initial entry.

• Theory of Utility

  • Rationality has a different meaning in economics than it does in common parlance.
  • Whenever an individual is to choose between a group of options, they are rational if they choose the option that, all else equal, gives the greatest utility.
  • If, when everything is taken into account, one decision provides the greatest utility, which is equivalent to meaning that it is the most preferred, then we would expect the individual to take that most preferred option.

• Chronic Obstructive Pulmonary Disease (COPD)

  • In COPD, the greatest reduction in air flow occurs when breathing out (during expiration), because the pressure in the chest tends to compress rather than expand the airways.
  • This is particularly common during exercise, when breathing has to be faster.
  • The diagnosis of COPD is confirmed by spirometry, a test that measures the forced expiratory volume in one second (FEV1), which is the greatest volume of air that can be breathed out in the first second of a large breath.
  • Spirometry also measures the forced vital capacity (FVC), which is the greatest volume of air that can be breathed out in a whole, large breath.

• Path distances

  • The most common is probably the geodesic path distance.
  • The farness figures can be re-expressed as nearness (the reciprocal of far-ness) and normed relative to the greatest nearness observed in the graph (here, the inCloseness of actor 7).