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greatest common factor

greatest common factor

4.4
The largest number that divides evenly into two or more whole numbers without leaving a remainder
  • noun
  • /ˈɡreɪtɪst ˈkɒmən ˈfæktər/
  • Specialized
translation icon : máximo común divisor
  • The greatest common factor of 12, 30, and 54 is 6.

That was the greatest common factor of both terms.

Examples

  • The greatest common factor of 24 and 36 is 12.

  • That was the greatest common factor of both terms.

  • Let them discover the greatest common factor.

    Blog text (17)
  • And the GCF is pretty much identified as the greatest common factor, the number that divides into both of those terms.

  • The greatest common factor between 75 and 105 is 15.

Synonyms

greatest common divisor
vsgreatest common factor
  • Specialized
5.5

The biggest whole number that divides two or more numbers exactly

uses a different ordinary wording for the same mathematical idea
highest common factor
vsgreatest common factor
  • UK
3.5

The largest positive whole number that divides two or more numbers exactly

uses a different ordinary wording for the same mathematical idea
GCD
vsgreatest common factor
  • Specialized
5.8

The largest number that divides two or more numbers exactly

is the full phrase written out rather than a shortened label

Surface Forms

Morphology

greatest + common + factor

The meaning is directly compositional: 'greatest' (largest), 'common' (shared by the numbers), and 'factor' (a number that divides another exactly) combine to yield the largest number that divides all the given integers. This mathematical compound follows a transparent, cross-linguistically common naming pattern, so a B1 learner who knows the constituent words will very likely infer the correct meaning.

Etymology

Greatest common factor creates a clear picture: imagine two piles of blocks and you want to split each pile into equal small groups. The factor is the size of each group, common means it works for both piles, and greatest means the biggest such group, so it is the 'largest number that divides' both numbers exactly.