Greatest Common Factor (GCF)
The GCF (also called GCD, greatest common divisor) of two or more numbers is the largest number that divides all of them exactly, with no remainder. It’s commonly used to simplify fractions — dividing both the numerator and denominator by their GCF reduces a fraction to its simplest form.
To calculate this value automatically for any pair of numbers, try our free GCF Calculator tool.
Least Common Multiple (LCM)
The LCM of two or more numbers is the smallest number that all of them divide into exactly. It’s commonly used when adding or comparing fractions with different denominators — finding a common denominator is really finding the LCM of the existing denominators.
To compute least common multiples instantly, use our free LCM Calculator tool.
Prime factorization
Prime factorization breaks a number down into the prime numbers that multiply together to produce it (for example, 60 = 2 × 2 × 3 × 5). This is the underlying technique behind calculating both GCF and LCM systematically for larger numbers, rather than guessing — you compare the prime factors two numbers share (for GCF) or combine all the prime factors needed to cover both numbers (for LCM).
For more details on mathematical factor definitions, you can check the Wikipedia Prime Factorization Reference Page.
Where these show up outside the classroom
- Simplifying ratios and fractions in recipes, finance, and measurements
- Scheduling problems — for example, figuring out when two repeating events next coincide (an LCM problem)
- Dividing items or groups evenly (a GCF problem)
- Cryptography and computer science rely heavily on prime factorization concepts, though at a much larger scale