Greatest Common Factor (GCF)
Definition: The "greatest common factor" (often abbreviated as GCF) is a mathematical term. It refers to the largest number that can divide two or more integers (whole numbers) without leaving a remainder. In simpler terms, it is the biggest number that is a common factor of the given numbers.
Usage Instructions: When you want to find the GCF of two or more numbers, you look for the largest number that can evenly divide all of them.
Example:Let's find the GCF of 12 and 18: 1. The factors of 12 are: 1, 2, 3, 4, 6, 12 2. The factors of 18 are: 1, 2, 3, 6, 9, 18 3. The common factors are: 1, 2, 3, 6 4. The greatest common factor is 6, because it is the largest number in the list of common factors.
Advanced Usage: In more advanced mathematics, finding the GCF is useful for simplifying fractions. For example, if you want to simplify the fraction 24/36, you can divide both the numerator (24) and the denominator (36) by their GCF, which is 12. So, 24 ÷ 12 = 2 and 36 ÷ 12 = 3, giving you the simplified fraction 2/3.
Word Variants: - Common factor: Any number that divides two or more numbers without a remainder. - Factor: A number that divides another number completely.
Different Meanings:In this context, "greatest common factor" specifically refers to mathematics. However, the word "factor" can also mean an element or part of something that contributes to a result. For example, "One factor of success is hard work."
Synonyms: - Highest common factor (HCF) - Greatest divisor
Idioms and Phrasal Verbs:While "greatest common factor" doesn't have idioms or phrasal verbs associated with it, you may encounter phrases like "finding common ground" in discussions, which metaphorically refers to finding shared interests or agreements, similar to finding common factors in numbers.