The Greatest Common Factor (GCF) is the largest positive integer that divides two or more numbers without a remainder.

For example, the GCF of 24 and 36 is 12, because 12 is the largest number that divides both 24 and 36 without a remainder.

Euclidean Algorithm

This method uses repeated division to find the GCF. For two numbers a and b (where a > b), divide a by b to get a remainder r. Then set a = b and b = r, and repeat until r = 0. The last non-zero remainder is the GCF.

Prime Factorization

Break down each number into its prime factors, then multiply the common prime factors (using the smallest exponent for each).

Listing Factors

List all factors of each number and identify the largest common factor.

• Simplifying Fractions: Divide both numerator and denominator by their GCF to reduce fractions to lowest terms.
• Factoring Expressions: Use GCF to factor algebraic expressions.
• Problem Solving: Useful in various real-life scenarios like dividing items into equal groups.