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Greatest Common Factor

The Greatest Common Factor

is the largest integer that is a factor of two or more integers.

The acronym GCF is often used.

In order to find the GCF you must first find the prime factors of the integers, and then compare what they have in common and take their largest factor.

greatest common factors example with the integers 8, 12 and 24


the GCF between 8 and 12 is (red marks) 2 x 2 = 4

the GCF between 8 and 24 is (blue marks) 2 x 2 x 2 = 8

the GCF between 8, 12 and 24 you know?















The Greatest Common Factor is a concept easier to understand than its name is to remember, yet not so easy to digest immediately, really.

Like for the whole of mathematics and algebra, You must exercise it!

It is of paramount importance in algebra. It helps simplify fractions. It goes together with the Least Common Multiple (LCM).

Here is a calculator for you to use for both calculations (use it NOT as shortcut, but as way to check your manual answers!)

First Number: Second Number:
Third Number (not required):

Greatest Common Factor (GCF):
Least Common Multiplier (LCM):


rupted movement of thought, with distinct intuition of each
thing; just as we know that the last link of a long chain holds to
the first, although we can not take in with one glance of the eye
the intermediate links, provided that, after having run over
them in succession, we can recall them all, each as being joined to
its fellows, from the first up to the last. Thus we distinguish
intuition from deduction, inasmuch as in the latter case there is
conceived a certain progress or succession, while it is not so in
the former; . . . whence it follows that primary propositions,
derived immediately from principles, may be said to be known,
according to the way we view them, now by intuition, now by
deduction; although the principles themselves can be known
only by intuition, the remote consequences only by deduction.


Rules for the Direction of the Mind, Philosophy
of D. [Torrey] (New York, 1892), pp. 64, 65.

220. Analysis and natural philosophy owe their most impor-
tant discoveries to this fruitful means, which is called induction.
Newton was indebted to it for his theorem of the binomial and
the principle of universal gravity. LAPLACE.

A Philosophical Essay on Probabilities [Tru-
scott and Emory] (New York 1902), p. 176.

221. There is in every step of an arithmetical or algebraical
calculation a real induction, a real inference from facts to facts,
and what disguises the induction is simply its comprehensive
nature, and the consequent extreme generality of its language.

System of Logic, Bk. 2, chap. 6, 2.


Memorabilia mathematica; or, The philomath's quotation-book - Moritz, Robert Édouard, 1868-1940

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