Unique Prime Factorization
The Fundamental Theorem of Arithmetic states that every natural number greater than 1 can be written as a product of prime numbers, and that up to rearrangement of the factors, this product is unique. This is called the prime factorization (or PF for short) of the number.
Example:
36 = 6 × 6 = 9 × 4 = 12 × 3 = 18 × 2,
but all are equal to 2 × 2 × 3 × 3.
This is the PF of 36, often written with exponents:
36 = 22 × 32
You can use these PFs to figure out GCFs (Greatest Common Factors), LCMs (Least Common Multiples), and the number (and sum) of divisors of n.
