common divisor

Thân thiện

The teacher writes the common divisor of 12 and 18 on the board.

Definition

1. Noun:
   • A number that divides two or more other numbers without leaving a remainder: A "common divisor" is an integer that is a factor of each number in a given set of integers. The largest such number is called the greatest common divisor (GCD).

Usage

• The term "common divisor" is primarily used in mathematics, specifically in number theory and arithmetic.
• It is used to find shared factors between numbers, which is useful for simplifying fractions or solving certain equations.
• The concept is foundational for understanding the greatest common divisor (GCD).

Examples

• Noun:
  • The numbers 12 and 18 have several common divisors, including 1, 2, 3, and 6.
  • To simplify the fraction 8/12, we first find a common divisor of 8 and 12, which is 4.
  • If two numbers share no common divisor greater than 1, they are said to be relatively prime.

Advanced Usage

• "Greatest common divisor (GCD)": The largest common divisor shared by a set of numbers.
  • The greatest common divisor of 24 and 36 is 12.
• "Common divisor theorem": A principle in number theory related to divisibility and linear combinations.

Variants and Related Words

• Divisor (Noun): A number that divides another number exactly.
  • In the equation 15 ÷ 3 = 5, the number 3 is a divisor of 15.
• Greatest Common Divisor (GCD) (Noun): The largest common divisor.
• Common Factor (Noun): A synonym for "common divisor."

Synonyms

• Common factor: A number that divides two or more numbers exactly.
• Common measure: (Less common) A term sometimes used interchangeably with common divisor.

Antonyms

• Relatively prime: Describing a set of numbers whose only common divisor is 1.
  • The numbers 9 and 16 are relatively prime.

Học thuật

Noun

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

Từ đồng nghĩa

• common factor
• common measure