common divisor
Definition
- 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.
Noun
-
an integer that divides two (or more) other integers evenly
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