greatest common factor

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greatest common factor

A student calculates the greatest common factor of two numbers on a worksheet.

Definition
  1. Noun:
    • The largest integer that divides without remainder into a set of integers: The "greatest common factor" (GCF) is the largest positive integer that is a factor of two or more given integers. It is also commonly called the greatest common divisor (GCD).
Usage
  • The term "greatest common factor" is used primarily in mathematics, specifically in arithmetic and number theory.
  • It is used to find the largest number that can exactly divide a set of numbers, which is useful for simplifying fractions or solving certain problems.
Examples
  • Noun:
    • To simplify the fraction 12/18, first find the greatest common factor of 12 and 18, which is 6.
    • The greatest common factor of 8, 12, and 20 is 4.
    • Finding the greatest common factor is a fundamental skill in elementary mathematics.
Advanced Usage
  • "To find the greatest common factor": This is the standard phrase for the mathematical operation.
    • You can find the greatest common factor by listing all the factors of each number and identifying the largest one common to all lists.
  • The concept is foundational for understanding the Euclidean algorithm, a more efficient method for finding the GCF of two numbers.
Variants and Related Words
  • Greatest Common Divisor (GCD) (n): A completely synonymous term for "greatest common factor."
  • Highest Common Factor (HCF) (n): Another synonymous term, commonly used in some regions.
  • Common Factor (n): Any integer that divides two or more numbers without a remainder. The GCF is the of these.
  • Factor (n): A number that divides another number exactly.
Synonyms
  • Greatest Common Divisor (GCD)
  • Highest Common Factor (HCF)
Related Phrases
  • "Reduce to lowest terms": This phrase often involves using the GCF to simplify a fraction.
    • After finding the greatest common factor, you can reduce the fraction to its lowest terms.
greatest common factor

A student calculates the greatest common factor of two numbers on a worksheet.

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

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