The greatest common factor is a mathematical concept that refers to the largest number that divides two or more integers without leaving any remainder. Some synonyms for the greatest common factor include the highest common factor, the greatest common divisor, and the highest common factor. The GCF is often used when simplifying fractions, factoring polynomials, and solving equations. It is an essential concept in mathematics and has numerous applications in real-life situations, such as finding the common denominator in cooking recipes or determining the number of tiles needed to cover a floor. Regardless of the term used, the GCF remains the same and plays a significant role in solving mathematical problems.