common factor
Definition
- Noun:
- Mathematics: An integer that divides two or more other integers evenly, leaving no remainder. It is a number that is a factor of each of the given numbers.
Usage
- The term "common factor" is used primarily in mathematics, specifically in arithmetic and algebra. It describes a shared divisor of a set of integers.
- It is often used when simplifying fractions (by dividing the numerator and denominator by their greatest common factor) or when factoring algebraic expressions.
Examples
- Noun:
- The numbers 12 and 18 share several common factors, including 1, 2, 3, and 6.
- To reduce the fraction 8/12 to its simplest form, find the greatest common factor of 8 and 12, which is 4.
- Finding the common factors is the first step in factoring a polynomial expression.
Advanced Usage
- "Greatest Common Factor (GCF)" or "Highest Common Factor (HCF)": The largest integer that is a common factor of a given set of numbers.
- The greatest common factor of 24 and 36 is 12.
- "Common factor analysis": A statistical method, though this is a compound term where "common factor" is part of a specialized name.
Variants and Related Words
- Factor (noun): A number or algebraic expression that divides another number or expression evenly.
- 3 is a factor of 15.
- Divisor (noun): A synonym for "factor" in this context.
- Common divisor (noun): A term interchangeable with "common factor."
Synonyms
- Common divisor: A number that divides two or more integers without a remainder.
Antonyms
- Relatively prime numbers: A pair or set of numbers whose greatest common factor is 1, meaning they share no common factors other than 1.
Noun
-
an integer that divides two (or more) other integers evenly
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