greatest common factor

Meaning

1. 1nouncountablemathematics

   The largest whole number that divides exactly into two or more given whole numbers.

   Grammar: Countable; often used with the definite article: the greatest common factor of 12 and 18.

   Patterns

   • the greatest common factor of two numbers
   • find the greatest common factor
   • greatest common factor of something and something

   The greatest common factor of 12 and 18 is 6.

   To simplify the fraction 8/12, divide both parts by their greatest common factor, which is 4.

   She asked the class to find the greatest common factor of 24 and 36.

Word forms

Common combinations

find the greatest common factor

First find the greatest common factor of the two numbers.

the greatest common factor of

What is the greatest common factor of 15 and 25?

greatest common factor method

The greatest common factor method makes simplifying fractions easier.

use the greatest common factor

Use the greatest common factor to reduce the fraction to lowest terms.

Synonyms and how they differ

highest common factor

The usual British term for the same idea; it is more common in UK classrooms.

greatest common divisor

A more formal or technical term, often used in advanced math and computer science.

Opposites

Word family

factor noun

A number that divides exactly into another number.

common factor noun

A number that divides exactly into two or more numbers.

Commonly confused: greatest common factor or least common multiple?

Practice

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Write a sentence using “greatest common factor”, then check it and compare it with the examples above.

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