common factor

Thân thiện

The number 3 is a common factor of 6 and 9.

Definition

1. 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.

Học thuật

Noun

1. an integer that divides two (or more) other integers evenly

Từ đồng nghĩa

• common divisor
• common measure