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.

Noun

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