Prime Factors, HCF and LCM

Number

Prime numbers are those divisible by nothing except themselves and 1, giving them a factor count of exactly two
The primes begin 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and continue without end
Every even number beyond 2 has 2 as a third factor, which leaves 2 as the sole even prime
1 is not prime, because it has a single factor rather than two

Broken down far enough, any integer is a product of primes alone, and those primes are its prime factors
- 30 is built from 2, 3 and 5, since 2 × 3 × 5 = 30
Every integer above 1 has exactly one set of prime factors, whatever route is taken to find them
This uniqueness is what allows prime factors to be used for comparing two numbers