greatest common divisor

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Term: Greatest Common Divisor (GCD)

Part of Speech: Noun

Definition: The greatest common divisor is the largest whole number (integer) that can evenly divide two or more numbers without leaving a remainder. In simpler terms, it’s the biggest number that fits into each of the numbers in a group exactly.

Usage Instructions:

• The term is often used in mathematics, especially in topics related to fractions, simplifying ratios, and solving problems involving divisibility.
• When you have a set of numbers, you can find the GCD to help simplify problems or fractions.

Example:

• Let’s say you have the numbers 12 and 16. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 16 are 1, 2, 4, 8, and 16. The largest number that appears in both lists is 4. Therefore, the greatest common divisor of 12 and 16 is 4.

Advanced Usage:

• In mathematics, finding the GCD can be done using methods like prime factorization or the Euclidean algorithm.
• The GCD is important in simplifying fractions. For example, to simplify 8/12, you would divide both the numerator (8) and the denominator (12) by their GCD, which is 4. This gives you 2/3.

Word Variants:

• Common Divisor: A number that can divide two or more numbers.
• Highest Common Factor (HCF): Another term often used interchangeably with greatest common divisor.

Different Meanings:

• In a different context, "divisor" alone refers to any number that divides another number, not necessarily the greatest.

Synonyms:

• Highest Common Factor (HCF)
• Common Factor

Related Terms:

• Least Common Multiple (LCM): The smallest number that is a multiple of two or more numbers, which is often discussed alongside GCD.

Idioms and Phrasal Verbs:

• While there aren't specific idioms or phrasal verbs directly related to "greatest common divisor," you might hear the term in mathematical discussions or educational contexts.

Summary:

The greatest common divisor is a key concept in mathematics that helps in simplifying numbers and understanding their relationships.

Academic

Noun

1. the largest integer that divides without remainder into a set of integers

Synonyms

• greatest common factor
• highest common factor