- The largest factor that is a factor of two or more integers or terms
- Example: 7 is the greatest common factor between 14 , 21, and 35
- Applications: simplifying fractions, factoring polynomials
- With respect to fractions, the GCF between the numerator and denominator is called the Greatest Common Divisor or GCD
- Methods of finding GCF between integers: List the factors of each integer, prime factorization of each integer
Greatest Common Factor (Wikipedia)
In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, .
In the name "greatest common divisor", the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), etc. Historically, other names for the same concept have included greatest common measure.
This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see § In commutative rings below).